symmetry preserving discretization of navier stokes equations on collocated unstructured grids a fully conservative discretization is presented in this paper the same principles followed by verstappen and veldman 2003 3 are generalized for unstructured meshes here a collocated mesh scheme is preferred over a staggered one due to its simpler form for such meshes the basic idea behind this approach remains the same mimicking the crucial symmetry properties of the underlying differential operators i e the convective operator is approximated by a skew symmetric matrix and the diffusive operator by a symmetric positive definite matrix a novel approach to eliminate the checkerboard spurious modes without introducing any non physical dissipation is proposed to do so a fully conservative regularization of the convective term is used the supraconvergence of the method is numerically showed and the treatment of boundary conditions is discussed finally the new discretization method is successfully tested for a buoyancy driven turbulent flow in a differentially heated cavity

correlation structure of the landscape of the graph bipartitioning problem the relaxation of random walks and the autocorrelation function on the landscape of the graph bipartitioning problem are calculated

integral equation preconditioning for the solution of poisson s equation on geometrically complex regions this paper is concerned with the implementation and investigation of integral equation based solvers as preconditioners for finite difference discretizations of poisson equations in geometrically complex domains the target discretizations are those associated with cut out grids we discuss such grids and also describe a software structure which enables their rapid construction computational results are presented

some periodic convolutional codes better than any fixed code corresp some n o 2 k o 1 noncatastrophic periodic convolutional codes with memory m 4 are given that have the same free distance d infty as the best fixed code but have both a smaller number of paths of weight d infty per time instant and a smaller average number of information bit errors per such path for periods t 2 3 4 and 5 it is also shown that an n 0 k 0 code of period t is equivalent to a fixed code with parameters tn 0 tk 0

iterative across time solution of linear differential equations krylov subspace versus waveform relaxation the aim of this paper is two fold first we propose an efficient implementation of the continuous time waveform relaxation wr method based on block krylov subspaces second we compare this new wr krylov implementation against krylov subspace methods combined with the shift and invert sai technique some analysis and numerical experiments are presented since the wr krylov and sai krylov methods build up the solution simultaneously for the whole time interval and there is no time stepping involved both methods can be seen as iterative across time methods the key difference between these methods and standard time integration methods is that their accuracy is not directly related to the time step size

error exponents of typical random trellis codes in continuation to an earlier work where error exponents of typical random codes were studied in the context of general block coding with no underlying structure here we carry out a parallel study on typical random time varying trellis codes focusing on a certain range of low rates by analyzing an upper bound to the error probability of the typical random trellis code using the method of types we first derive a csiszar style error exponent formula with respect to the constraint length which allows to characterize properties of good codes and dominant error events we also derive a gallager style form which turns out to be related to the expurgated error exponent the main result is further extended to channels with memory and mismatch

solution adaptive cartesian cell approach for viscous and inviscid flows a cartesian cell based approach for adaptively refined solutions of the euler and navier stokes equations in two dimensions is presented grids about geometrically complicated bodies are generated automatically by the recursive subdivision of a single cartesian cell encompassing the entire flow domain where the resulting cells intersect bodies polygonal cut cells are created using modified polygon clipping algorithms the grid is stored in a binary tree data structure that provides a natural means of obtaining cell to cell connectivity and of carrying out solution adaptive mesh refinement the euler and navier stokes equations are solved on the resulting grids using a finite volume formulation the convective terms are up winded a linear reconstruction of the primitive variables is performed providing input states to an approximate riemann solver for computing the fluxes between neighboring cells the results of a study comparing the accuracy and positivity of two classes of cell centered viscous gradient reconstruction procedures is briefly summarized adaptively refined solutions of the navier stokes equations are shown using the more robust of these gradient reconstruction procedures where the results computed by the cartesian approach are compared to theory experiment and other accepted computational results for a series of low and moderate reynolds number flows

assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows in this work we study the performance of some variational multiscale models vms in the large eddy simulation les of turbulent flows we consider vms models obtained by different subgrid scale approximations which include either static or dynamic subscales linear or nonlinear multiscale splitting and different choices of the subscale space after a brief review of these models we discuss some implementation aspects particularly relevant to the simulation of turbulent flows namely the use of a skew symmetric form of the convective term and the computation of projections when orthogonal subscales are used we analyze the energy conservation and numerical dissipation of the alternative vms formulations which is numerically evaluated in the numerical study we have considered three well known problems the decay of homogeneous isotropic turbulence the taylor green vortex problem and the turbulent flow in a channel we compare the results obtained using different vms models paying special attention to the effect of using orthogonal subscale spaces the vms results are also compared against classical les scheme based on filtering and the dynamic smagorinsky closure altogether our results show the tremendous potential of vms for the numerical simulation of turbulence further we study the sensitivity of vms to the algorithmic constants and analyze the behavior in the small time step limit we have also carried out a computational cost comparison of the different formulations out of these experiments we can state that the numerical results obtained with the different vms formulations as far as they converge are quite similar however some choices are prone to instabilities and the results obtained in terms of computational cost are certainly different the dynamic orthogonal subscales model turns out to be best in terms of efficiency and robustness

parallel direct poisson solver for discretisations with one fourier diagonalisable direction in the context of time accurate numerical simulation of incompressible flows a poisson equation needs to be solved at least once per time step to project the velocity field onto a divergence free space due to the non local nature of its solution this elliptic system is one of the most time consuming and difficult to parallelise parts of the code in this paper a parallel direct poisson solver restricted to problems with one uniform periodic direction is presented it is a combination of a direct schur complement based decomposition dsd and a fourier diagonalisation the latter decomposes the original system into a set of mutually independent 2d systems which are solved by means of the dsd algorithm since no restrictions are imposed in the non periodic directions the overall algorithm is well suited for solving problems discretised on extruded 2d unstructured meshes the load balancing between parallel processes and the parallelisation strategy are also presented and discussed the scalability of the solver is successfully tested using up to 8192 cpu cores for meshes with up to 10 9 grid points finally the performance of the dsd algorithm as 2d solver is analysed by direct comparison with two preconditioned conjugate gradient methods for this purpose the turbulent flow around a circular cylinder at reynolds numbers 3900 and 10 000 are used as problem models

adaptive mesh finite volume calculation of 2d lid cavity corner vortices abstract an anisotropic refinement criterion suitable for finite volume methods is presented and navier stokes solutions are reported for the lid driven cavity flow configuration at re 1000 with adaptive anisotropic meshes h refinement the a posteriori error estimation criterion is based on the assessment of the goodness of fit of the least squares regression used to perform the variables profile reconstruction and it is capable of detecting both large scale and small scale flow phenomena the criterion allowed to capture in detail the large scale flow structure and also the sequence of creeping flow small sharp corner s 1 eddies up to the fourth corner vortex in addition to the primary cavity vortex the smallest corner vortex detected is o 10 16 smaller in velocity magnitude compared with the cavity primary recirculation flow

reduced aliasing formulations of the convective terms within the navier stokes equations for a compressible fluid the effect on aliasing errors of different formulations describing the cubically nonlinear convective terms within the discretized navier stokes equations is examined in the presence of a non trivial density spectrum fourier analysis shows that the existing skew symmetric forms of the convective term result in reduced aliasing errors relative to the conservation form several formulations of the convective term including a new formulation proposed for cubically nonlinear terms are tested in direct numerical simulation dns of decaying compressible isotropic turbulence both in chemically inert small density fluctuations and reactive cases large density fluctuations and for different degrees of resolution in the dns of reactive turbulent flow the new cubic skew symmetric form gives the most accurate results consistent with the spectral error analysis and at the lowest cost in marginally resolved dns and les poorly resolved by definition the new cubic skew symmetric form represents a robust convective formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high order dissipative filters

energy conserving runge kutta methods for the incompressible navier stokes equations energy conserving methods have recently gained popularity for the spatial discretization of the incompressible navier stokes equations in this paper implicit runge kutta methods are investigated which keep this property when integrating in time firstly a number of energy conserving runge kutta methods based on gauss radau and lobatto quadrature are constructed these methods are suitable for convection dominated problems such as turbulent flows because they do not introduce artificial diffusion and are stable for any time step secondly to obtain robust time integration methods that work also for stiff problems the energy conserving methods are extended to a new class of additive runge kutta methods which combine energy conservation with l stability in this class the radau iia b method has the best properties results for a number of test cases on two stage methods indicate that for pure convection problems the additive radau iia b method is competitive with the gauss methods however for stiff problems such as convection dominated flows with thin boundary layers both the higher order gauss and radau iia b method suffer from order reduction overall the gauss methods are the preferred method for energy conserving time integration of the incompressible navier stokes equations

a fixed mesh method for incompressible flow structure systems with finite solid deformations a fixed mesh algorithm is proposed for simulating flow structure interactions such as those occurring in biological systems in which both the fluid and solid are incompressible and the solid deformations are large several of the well known difficulties in simulating such flow structure interactions are avoided by formulating a single set of equations of motion on a fixed eulerian mesh the solid s deformation is tracked to compute elastic stresses by an overlapping lagrangian mesh in this way the flow structure interaction is formulated as a distributed body force and singular surface force acting on an otherwise purely fluid system these forces which depend on the solid elastic stress distribution are computed on the lagrangian mesh by a standard finite element method and then transferred to the fixed eulerian mesh where the joint momentum and continuity equations are solved by a finite difference method the constitutive model for the solid can be quite general for the force transfer standard immersed boundary and immersed interface methods can be used and are demonstrated we have also developed and demonstrated a new projection method that unifies the transfer of the surface and body forces in a way that exactly conserves momentum the interface is still effectively sharp for this approach the spatial convergence of the method is observed to be between first and second order as in most immersed boundary methods for membrane flows the algorithm is demonstrated by the simulations of an advected elastic disk a flexible leaflet in an oscillating flow and a model of a swimming jellyfish

comparison of some lie symmetry based integrators lie symmetry based integrators are constructed in order to preserve the local invariance properties of the equations the geometrical methods leading to discretized equations for numerical computations involve many different concepts therefore they give rise to numerical schemes that vary in the accuracy in the computational cost and in the implementation in this paper a comparison is made between some alternative lie symmetry based methods illustrated on the example of the burgers equation the importance of the symmetry preservation is numerically highlighted

finite surface discretization for incompressible navier stokes equations and coupled conservation laws abstract we present a new finite surface discretization fsd aiming at the incompressible navier stokes equations nse and other coupled conservation laws this discretization defines the velocities as surfaced averaged values living on the faces of the pressure volumes in which the mass is set to be conserved consequently the calculation of the mass balance on these control volumes is exact which allows more accurate information to be kept in the velocity field and produces a very accurate prediction of the pressure in the next time step the proposed discretization reduces the stencil size of the poisson equation in the projection method compared to the finite volume and finite difference discretizations due to highly accurate mass conservation the compact sixth order approximation of fsd can be used with an explicit fourth order pressure treatment this property greatly reduces the cost and complexity of the implementation we present the discrete evolution equation of the surface averaged velocities together with the enforcement of mass conservation and the solution procedure for the pressure the approximation of the nse under this new discretization uses a combination of finite difference and finite volume methods the proposed method is validated using standard laminar test cases we identify the conditions under which a fourth order pressure treatment can support the sixth order and eighth order approximations of the convection term using fourier analysis the performance of the method is evaluated on turbulent channel flows up to friction reynolds number of 950 the quantitative relationships between the accuracy of the solution and grid size are identified we present two performance indices for comparison with other methods at the error level of 1 per mille the proposed method is 28 times faster than the classic second order scheme

a staggered compact finite difference formulation for the compressible navier stokes equations in this paper a compact high order up to 12th order numerical method to solve the compressible navier stokes equations will be presented a staggered arrangement of the variables has been used it is shown that the method is not only very accurate but numerically also very stable even in the case that not all the energy containing scales in the flow are resolved this in contrast to standard collocated compact finite difference methods some results for a turbulent non reacting and a reacting jet with a reynolds number of 10 000 and a mach number of 0 5 are reported

energy preserving turbulent simulations at a reduced computational cost energy conserving discretizations are widely regarded as a fundamental requirement for high fidelity simulations of turbulent flows the skew symmetric splitting of the nonlinear term is a well known approach to obtain semi discrete conservation of energy in the inviscid limit however its computation is roughly twice as expensive as that of the divergence or advective forms alone a novel time advancement strategy that retains the conservation properties of skew symmetric based schemes at a reduced computational cost has been developed this method is based on properly constructed runge kutta schemes in which a different form advective or divergence for the convective term is adopted at each stage a general framework is presented to derive schemes with prescribed accuracy on both solution and energy conservation simulations of homogeneous isotropic turbulence show that the new procedure is effective and can be considerably faster than skew symmetric based techniques

isotropic finite volume discretization finite volume methods traditionally employ dimension by dimension extension of the one dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured cartesian mesh in multiple dimensions this simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution the resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines in this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions respectively it is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next nearest and next next nearest neighbors in three dimensions use of these isotropic expressions alone in a standard finite volume framework however is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and or spatially non uniform the rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms while preserving the formal order of accuracy and discrete conservation of the original finite volume method are developed numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method prominent anisotropic errors such as spurious asymmetric distortions on a circular reaction diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization furthermore for a given spatial resolution a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization c 2014 elsevier inc all rights reserved

an analysis of numerical errors in large eddy simulations of turbulence the reliability of numerical simulations of turbulence depend on our ability to quantify and control discretization errors in the classical literature on error analysis typically simple linear equations are studied estimates of errors derived from such analyses depend on the assumption that each dependent variable can be characterized by a unique amplitude and scale of spatial variation that can be normalized to unity this assumption is not valid for strongly nonlinear problems such as turbulence where nonlinear interactions rapidly redistribute energy resulting in the appearance of a broad continuous spectrum of amplitudes in such situations the numerical error as well as the subgrid model can change with grid spacing in a complicated manner that cannot be inferred from the results of classical error analysis in this paper a formalism for analyzing errors in such nonlinear problems is developed in the context of finite difference approximations for the navier stokes equations when the flow is fully turbulent analytical expressions for the power spectra of these errors are derived by exploiting the joint normal approximation for turbulent velocity fields these results are applied to large eddy simulation of turbulence to obtain quantitative bounds on the magnitude of numerical errors an assessment of the significance of these errors in made by comparing their magnitudes with that of the nonlinear and subgrid terms one method of controlling the errors is suggested and its effectiveness evaluated through quantitative measures although explicit evaluations are presented only for large eddy simulation the expressions derived for the power spectra of errors are applicable to direct numerical simulation as well

a shift transformation for fully conservative methods turbulence simulation on complex unstructured grids abstract operator transformations are presented that allow matrix operators for collocated variables to be transformed into matrix operators for staggered variables while preserving symmetries these shift transformations permit conservative skew symmetric convective operators and symmetric positive definite diffusive operators to be obtained for staggered variables using collocated operators shift transformations are not limited to uniform or structured meshes and this formulation leads to a generalization of the works of perot j comput phys 159 2000 58 and verstappen and veldman j comput phys 187 2003 343 a set of shift operators have been developed for and applied to a time adaptive cartesian mesh method with a fractional step algorithm the resulting numerical scheme conserves mass to machine error and conserves momentum and energy to second order in time a mass conserving interpolation is used for the variables during mesh adaptation the interpolation conserves momentum and energy to second order in space turbulent channel flow simulations were conducted at re 180 using direct numerical simulation dns the dns results from the adaptive method compare favourably with spectral dns results despite the use of a formally second order accurate scheme

a high order compact difference algorithm for half staggered grids for laminar and turbulent incompressible flows abstract the paper presents a novel efficient and accurate algorithm for laminar and turbulent flow simulations the spatial discretisation is performed with help of the compact difference schemes up to 10th order for collocated and half staggered grid arrangements the time integration is performed by a predictor corrector approach combined with the projection method for pressure velocity coupling at this stage a low order discretisation is introduced which considerably decreases the computational costs it is demonstrated that such approach does not deteriorate the solution accuracy significantly following boersma b j 13 the interpolation formulas developed for staggered uniform meshes are used also in the computations with a non uniform strongly varying nodes distribution in the proposed formulation of the projection method such interpolation is performed twice it is shown that it acts implicitly as a high order low pass filter and therefore the resulting algorithm is very robust its accuracy is first demonstrated based on simple 2d and 3d problems an inviscid vortex advection a decay of taylor green vortices a modified lid driven cavity flow and a dipole wall interaction in periodic flow problems the first two cases the solution accuracy exhibits the 10th order behaviour in the latter cases the 3rd and the 4th order is obtained robustness of the proposed method in the computations of turbulent flows is demonstrated for two classical cases a periodic channel with re 395 and re 590 and a round jet with re 21 000 the solutions are obtained without any turbulence model and also without any explicit techniques aiming to stabilise the solution the results are in a very good agreement with literature dns and les data both the mean and r m s values are predicted correctly

an energy stable scheme for incompressible navier stokes equations with periodically updated coefficient matrix abstract we present an energy stable scheme for simulating the incompressible navier stokes equations based on the generalized positive auxiliary variable gpav framework in the gpav reformulated system the original nonlinear term is replaced by a linear term plus a correction term where the correction term is put under control by an auxiliary variable the proposed scheme incorporates a pressure correction type strategy into the gpav procedure and it satisfies a discrete energy stability property the scheme entails the computation of two copies of the velocity and pressure within a time step by solving an individual de coupled linear equation for each of these field variables upon discretization the pressure linear system involves a constant coefficient matrix that can be pre computed while the velocity linear system involves a coefficient matrix that is updated periodically once every k 0 time steps in the current work where k 0 is a user specified integer the auxiliary variable being a scalar valued number is computed by a well defined explicit formula which guarantees the positivity of its computed values it is observed that the current method can produce accurate simulation results at large or fairly large time step sizes for the incompressible navier stokes equations the impact of the periodic coefficient matrix update on the overall cost of the method is observed to be small in typical numerical simulations several flow problems have been simulated to demonstrate the accuracy and performance of the method developed herein

coupling a wall diffusion model with an immersed boundary technique immersed boundary methods showed a good compliance for a wide range of complex inviscid and viscous flows moreover the high reynolds number regime still remains an open issue the paper describes a wall layer approach to answer the need of a model that goes beyond the actual capability of classical wall functions a near wall region is established that gets information from the outer flowfield and returns back the wall stress the latter is obtained by integrating simplified thin boundary layer equations along a normal to the wall subgrid in the outer zone the compressible reynolds averaged navier stokes equations are solved by means of a finite volume method on two or three dimensional cartesian meshes the classic validation test dealing with a high reynolds number flow over a flat plate is carried out a benchmark two dimensional complex flow is numerically investigated to assess the performance of the wall model in case of a pressure induced separation the results are compared with both experime

turbulent wall model for immersed boundary methods the paper describes the development of a wall model to extend the applicability of immersed boundary methods to high reynolds number flows a two layer approach based on a decomposition of the near wall region is adopted an outer region is governed by the compressible rans equations which are solved numerically by using a classical finite volume method in the proximity of the wall an inner zone is established and modelled by a simplified version of the thin boundary layer equations the simulation platform is based on cartesian meshes and an immersed boundary technique it is able to solve the steady euler rans equations in two and three dimensional coordinates the robustness and the accuracy of the methodology are discussed at present this work represents the last advance of a research activity whose final goal is a fast pre design tool for aeronautical industrial applications

explicit runge kutta schemes for incompressible flow with improved energy conservation properties the application of pseudo symplectic runge kutta methods to the incompressible navier stokes equations is discussed in this work in contrast to fully energy conserving implicit methods these are explicit schemes of order p that preserve kinetic energy to order q with q p use of explicit methods with improved energy conservation properties is appealing for convection dominated problems especially in case of direct and large eddy simulation of turbulent flows a number of pseudo symplectic methods are constructed for application to the incompressible navier stokes equations and compared in terms of accuracy and efficiency by means of numerical simulations

maternal effects in molecular evolution we introduce a model of molecular evolution in which the fitness of an individual depends both on its own and on the parent s genotype the model can be solved by means of a nonlinear mapping onto the standard quasispecies model the dependency on the parental genotypes cancels from the mean fitness but not from the individual sequence concentrations for finite populations the position of the error threshold is very sensitive to the influence from parent genotypes in addition to biological applications our model is important for understanding the dynamics of self replicating computer programs

sequential quadratic programming sqp for optimal control in direct numerical simulation of turbulent flow the current work focuses on the development and application of an efficient algorithm for optimization of three dimensional turbulent flows simulated using direct numerical simulation dns or large eddy simulations and further characterized by large dimensional optimization parameter spaces the optimization algorithm is based on sequential quadratic programming sqp in combination with a damped formulation of the limited memory bfgs method the latter is suitable for solving large scale constrained optimization problems whose hessian matrices cannot be computed and stored at a reasonable cost we combine the algorithm with a line search merit function based on an l 1 norm to enforce the convergence from any remote point it is first shown that the proposed form of the damped l bfgs algorithm is suitable for solving equality constrained rosenbrock type functions then we apply the algorithm to an optimal control test problem that consists of finding the optimal initial perturbations to a turbulent temporal mixing layer such that mixing is improved at the end of a simulation time horizon t the controls are further subject to a non linear equality constraint on the total control energy dnss are used to resolve all turbulent scales of motion and a continuous adjoint formulation is employed to calculate the gradient of the cost functionals we compare the convergence speed of the sqp l bfgs algorithm to a conventional non linear conjugate gradient method i e the current standard in dns based optimal control and find that the sqp algorithm is more than an order of magnitude faster than the conjugate gradient method

the ls stag method a new immersed boundary level set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties this paper concerns the development of a new cartesian grid immersed boundary ib method for the computation of incompressible viscous flows in two dimensional irregular geometries in ib methods the computational grid is not aligned with the irregular boundary and of upmost importance for accuracy and stability is the discretization in cells which are cut by the boundary the so called cut cells in this paper we present a new ib method called the ls stag method which is based on the mac method for staggered cartesian grids and where the irregular boundary is sharply represented by its level set function this implicit representation of the immersed boundary enables us to calculate efficiently the geometry parameters of the cut cells we have achieved a novel discretization of the fluxes in the cut cells by enforcing the strict conservation of total mass momentum and kinetic energy at the discrete level our discretization in the cut cells is consistent with the mac discretization used in cartesian fluid cells and has the ability to preserve the five point cartesian structure of the stencil resulting in a highly computationally efficient method the accuracy and robustness of our method is assessed on canonical flows at low to moderate reynolds number taylor couette flow flows past a circular cylinder including the case where the cylinder has forced oscillatory rotations finally we will extend the ls stag method to the handling of moving immersed boundaries and present some results for the transversely oscillating cylinder flow in a free stream

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

conservative high order finite difference schemes for low mach number flows three finite difference algorithms are proposed to solve a low mach number approximation for the navier stokes equations these algorithms exhibit fourth order spatial and second order temporal accuracy they are dissipation free and thus well suited for dns and les of turbulent flows the key ingredient common to each of the methods presented is a poisson equation with variable coefficient that is solved for the hydrodynamic pressure this feature ensures that the velocity field is constrained correctly it is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation an existing set of finite difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non linear convective terms an algorithm which conserves mass momentum and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms

navier stokes calculations using cartesian grids i laminar flows a finite volume formulation for the navier stokes equations using cartesian grids is used to study flows past airfoils in addition to the solution of the complete equations solutions for two simplified versions of the governing equations were obtained and compared with those using body fitted grids results are presented for two airfoil sections naca 0012 and rae 2822 for a range of mach numbers angles of attack and reynolds numbers it is shown that the results are highly dependent on the smoothness of the surface grid without such smoothness the skin friction and pressure converge to nonuniform distributions on the other hand when surface cells with smoothly varying areas are used the results compare favorably with calculations employing body fitted grids urrently much of the work in computational fluid dynamics is focused on the solution of the navier stokes equations for increasingly complex airfoil and wing configura tions some of the issues being examined in these solutions are the efficiency of the algorithms the accuracy of the solutions and the generation of grids for complex geometries cartesian grids are being pursued as a simple alternative to complicated grid generation techniques for general configurations the successful implementation of cartesian grids for the solution of the euler equations1 demonstrated the simplicity and utility of these grids especially when multi element configurations were considered more recently use of cartesian grids was extended to the solution of the euler equations for flowfields around three dimensional geometries 2 the goal of the present work is to show the feasibility of using cartesian grids in the solution of the navier stokes equations for complex two dimensional configurations be cause of the many issues that were uncovered by the investi gation it was decided to limit the scope of the paper to laminar flows the algorithm employed is similar to that used in refs 1 and 2 and is based on the explicit runge kutta time stepping scheme of jameson et al 3 modifications pertaining to numerical damping were examined moreover the crucial influence of surface cells on the pressure and skin friction is investigated in detail a cell centered scheme is employed for such a scheme it is necessary to estimate the pressure and the various components of the stress tensor and the heat flux vector at the wall the wall pressure was estimated by extrapolation 1 2 two different methods for determining wall stresses are used and their effect on the solution is discussed in addition to the solution of the full equations two sim plified versions of the governing equations are considered

computation of solid liquid phase fronts in the sharp interface limit on fixed grids a finite difference formulation is applied to track solid liquid boundaries on a fixed underlying grid the interface is not of finite thickness but is treated as a discontinuity and is explicitly tracked the imposition of boundary conditions exactly on a sharp interface that passes through the cartesian grid is performed using simple stencil readjustments in the vicinity of the interface attention is paid to formulating difference schemes that are globally second order accurate in x and t error analysis and grid refinement studies are performed for test problems involving the diffusion and convection diffusion equations and for stable solidification problems issues concerned with stability and change of phase of grid points in the evolution of solid liquid phase fronts are also addressed it is demonstrated that the field calculation is second order accurate while the position of the phase front is calculated to first order accuracy furthermore the accuracy estimates hold for the cases where there is a property jump across the interface unstable solidification phenomena are simulated and an attempt is made to compare results with previously published work the results indicate the need to begin an effort to benchmark computations of instability phenomena

signal codes convolutional lattice codes the coded modulation scheme proposed in this paper has a simple construction an integer sequence representing the information is convolved with a fixed continuous valued finite impulse response fir filter to generate the codeword a lattice point due to power constraints the code construction includes a shaping mechanism inspired by precoding techniques such as the tomlinson harashima filter we naturally term these codes convolutional lattice codes or alternatively signal codes due to the signal processing interpretation of the code construction surprisingly properly chosen short fir filters can generate good codes with large minimal distance decoding can be done efficiently by sequential decoding or for better performance by bidirectional sequential decoding error analysis and simulation results indicate that for the additive white gaussian noise awgn channel convolutional lattice codes with computationally reasonable decoders can achieve low error rate close to the channel capacity

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

symmetrized compact scheme for receptivity study of 2d transitional channel flow in many physical problems one must maintain symmetry of numerical schemes the symmetry arising due to geometry and or physical conditions defining the flow the direct simulation of transitional plane poiseuille flow presents one such case that motivated the present study it has been shown here using the method of analyzing non periodic problems in sengupta et al 2003 that compact and other high accuracy schemes display strong directionality of the algorithm and such methods cannot be used for direct simulation of the physical flow this prevalent but unacceptable situation for dns is rectified in the present work and a new scheme is introduced that prevents this asymmetry from contaminating results the simulated transitional flow past 2d channel here using the new scheme are in agreement with experimental results and other recent views of sub critical instabilities

the sensitivity and accuracy of fourth order finite difference schemes on nonuniform grids in one dimension abstract we construct local fourth order finite difference approximations of first and second derivatives on nonuniform grids in one dimension the approximations are required to satisfy symmetry relationships that come from the analogous higher dimensional fundamental operators the divergence the gradient and the laplacian for example we require that the discrete divergence and gradient be negative adjoint of each other div grad and the discrete laplacian is defined as lap divgrad the adjointness requirement on the divergence and gradient guarantees that the laplacian is a symmetric negative operator the discrete approximations we derive are fourth order on smooth grids but the approach can be extended to create approximations of arbitrarily high order we analyze the loss of accuracy in the approximations when the grid is not smooth and include a numerical example demonstrating the effectiveness of the higher order methods on nonuniform grids

error threshold transition in the random energy model we perform a statistical analysis of the error threshold transition in quasispecies evolution on a random energy fitness landscape we obtain a precise description of the genealogical properties of the population through extensive numerical simulations we find a clear phase transition and can distinguish two regimes of evolution the first for low mutation rates is characterized by strong selection and the second for high mutation rates is characterized by quasineutral evolution

boundary treatment for fourth order staggered mesh discretizations of the incompressible navier stokes equations harlow and welch phys fluids 8 1965 2182 2189 introduced a discretization method for the incompressible navier stokes equations conserving the secondary quantities kinetic energy and vorticity besides the primary quantities mass and momentum this method was extended to fourth order accuracy by several researchers 25 14 21 in this paper we propose a new consistent boundary treatment for this method which is such that continuous integration by parts identities including boundary contributions are mimicked in a discrete sense in this way kinetic energy is exactly conserved even in case of non zero tangential boundary conditions we show that requiring energy conservation at the boundary conflicts with order of accuracy conditions and that the global accuracy of the fourth order method is limited to second order in the presence of boundaries we indicate how non uniform grids can be employed to obtain full fourth order accuracy

non linearly stable reduced order models for incompressible flow with energy conserving finite volume methods abstract a novel reduced order model rom formulation for incompressible flows is presented with the key property that it exhibits non linearly stability independent of the mesh of the full order model the time step the viscosity and the number of modes the two essential elements to non linear stability are 1 first discretise the full order model and then project the discretised equations and 2 use spatial and temporal discretisation schemes for the full order model that are globally energy conserving in the limit of vanishing viscosity for this purpose as full order model a staggered grid finite volume method in conjunction with an implicit runge kutta method is employed in addition a constrained singular value decomposition is employed which enforces global momentum conservation the resulting velocity only rom is thus globally conserving mass momentum and kinetic energy for non homogeneous boundary conditions a one time poisson equation is solved that accounts for the boundary contribution the stability of the proposed rom is demonstrated in several test cases furthermore it is shown that explicit runge kutta methods can be used as a practical alternative to implicit time integration at a slight loss in energy conservation

compact fourth order finite volume method for numerical solutions of navier stokes equations on staggered grids the development of a compact fourth order finite volume method for solutions of the navier stokes equations on staggered grids is presented a special attention is given to the conservation laws on momentum control volumes a higher order divergence free interpolation for convective velocities is developed which ensures a perfect conservation of mass and momentum on momentum control volumes three forms of the nonlinear correction for staggered grids are proposed and studied the accuracy of each approximation is assessed comparatively in fourier space the importance of higher order approximations of pressure is discussed and numerically demonstrated fourth order accuracy of the complete scheme is illustrated by the doubly periodic shear layer and the instability of plane channel flow the efficiency of the scheme is demonstrated by a grid dependency study of turbulent channel flows by means of direct numerical simulations the proposed scheme is highly accurate and efficient at the same level of accuracy the fourth order scheme can be ten times faster than the second order counterpart this gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost

a cartesian grid method with transient anisotropic adaptation a cartesian grid method with solution adaptive anisotropic refinement and coarsening is developed for simulating time dependent incompressible flows the cartesian grid cells and faces are managed using an unstructured data approach and algorithms are described for the time accurate transient anisotropic refinement and coarsening of the cells the governing equations are discretized using a collocated cell centered arrangement of velocity and pressure and advanced in time using the fractional step method significant savings in the memory requirement of the method can be realized by advancing the velocity field using a novel approximate factorization technique although an iterative technique is also presented the pressure poisson equation is solved using additive correction multigrid and an efficient coarse grid selection algorithm is presented finally the cartesian cell geometry allows the development of relatively simple analytic expressions for the optimal cell dimensions based on limiting the velocity interpolation error the overall method is validated by solving several benchmark flows including the 2d and 3d lid driven cavity flows and the 2d flow around a circular cylinder in this latter case an immersed boundary method is used to handle the embedded cylinder boundary

improved error exponent for time invariant and periodically time variant convolutional codes an improved upper bound on the error probability first error event of time invariant convolutional codes and the resulting error exponent is derived the improved error bound depends on both the delay of the code k and its width the number of symbols that enter the delay line in parallel b determining the error exponent of time invariant convolutional codes is an open problem while the previously known bounds on the error probability of time invariant codes led to the block coding exponent we obtain a better error exponent strictly better for b 1 in the limit b spl rarr spl infin our error exponent equals the yudkin viterbi 1967 1971 1965 exponent derived for time variant convolutional codes these results are also used to derive an improved error exponent for periodically time variant codes

numerical approximation of incompressible navier stokes equations based on an auxiliary energy variable abstract we present a numerical scheme for approximating the incompressible navier stokes equations based on an auxiliary variable associated with the total system energy by introducing a dynamic equation for the auxiliary variable and reformulating the navier stokes equations into an equivalent system the scheme satisfies a discrete energy stability property in terms of a modified energy and it allows for an efficient solution algorithm and implementation within each time step the algorithm involves the computations of two pressure fields and two velocity fields by solving several de coupled individual linear algebraic systems with constant coefficient matrices together with the solution of a nonlinear algebraic equation about a scalar number involving a negligible cost a number of numerical experiments are presented to demonstrate the accuracy and the performance of the presented algorithm

error threshold in simple landscapes we consider the quasispecies description of a population evolving in both the master sequence landscape where a single sequence is evolutionarily preferred over all others and the rem landscape where the fitness of different sequences is an independent identically distributed random variable we show that in both cases the error threshold is analogous to a first order thermodynamical transition where the overlap between the average genotype and the optimal one drops discontinuously to zero

high order finite volume approximations of differential operators on nonuniform grids abstract when computing numerical solutions to partial differential equations difference operators that mimic the crucial properties of the differential operators are usually more accurate than those that do not properties such as symmetry conservation stability and the duality relationships and identities between the gradient curl and divergence operators are all important using the finite volume method we have derived local accurate reliable and efficient difference methods t divergence gradient and curl operators are defined using a discrete versions of the divergence theorem and stokes theorem these methods are especially powerful on coarse nonuniform grids and in calculations where the mesh moves to track interfaces or shocks numerical examples comparing local second and fourth order finite volume approximations to conservation laws on very rough grids are used to demonstrate the advantages of the higher order methods

a co located incompressible navier stokes solver with exact mass momentum and kinetic energy conservation in the inviscid limit the incompressible navier stokes equations conserve mass momentum and kinetic energy in the inviscid limit therefore numerical methods should attempt to mimic these conservation properties as well there exists many well established methods with exact conservation properties based on staggered grids but existing methods based on co located grids introduce numerical dissipation in order to yield smooth pressure fields in the present work a novel method that utilizes null space vectors to yield a smooth pressure field is presented the method exactly preserves mass momentum and kinetic energy on co located grids

symmetry preserving discretization of turbulent flow we propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators i e the convective operator is represented by a skew symmetric coefficient matrix and the diffusive operator is approximated by a symmetric positive definite matrix mimicking crucial properties of differential operators forms in itself a motivation for discretizing them in a certain manner we give it a concrete form by noting that a symmetry preserving discretization of the navier stokes equations is stable on any grid and conserves the total mass momentum and kinetic energy for the latter the physical dissipation is to be turned off of coarse being stable on any grid the choice of the grid may be based on the required accuracy solely and the main question becomes how accurate is a symmetry preserving discretization its accuracy is tested for a turbulent flow in a channel by comparing the results to those of physical experiments and previous numerical studies the comparison is carried out for a reynolds number of 5600 which is based on the channel width and the mean bulk velocity based on the channel half width and wall shear velocity the reynolds number becomes 180 the comparison shows that with a fourth order symmetry preserving method a 64 64 32 grid suffices to perform an accurate numerical simulation

natural discretizations for the divergence gradient and curl on logically rectangular grids abstract this is the first in series of papers creating a discrete analog of vector analysis on logically rectangular nonorthogonal nonsmooth grids we introduce notations for 2 d logically rectangular grids describe both cell valued and nodal discretizations for scalar functions and construct the natural discretizations of vector fields using the vector components normal and tangential to the cell boundaries we then define natural discrete analogs of the divergence gradient and curl operators based on coordinate invariant definitions and interpret these formulas in terms of curvilinear coordinates such as length of elements of coordinate lines areas of elements of coordinate surfaces and elementary volumes we introduce the discrete volume integral of scalar functions the discrete surface integral and a discrete analog of the line integral and prove discrete versions of the main theorems relating these objects these theorems include the following the discrete analog of relationship div a 0 if and only if a curl b curl a 0 if and only if a grad if a grad then the line integral does not depend on path and if the line integral of a vector function is equal to zero for any closed path then this vector is the gradient of a scalar function last we define the discrete operators div grad and curl in terms of primitive differencing operators based on forward and backward differences and primitive metric operators related to multiplications of discrete functions by length of edges areas of surfaces and volumes of 3 d cells these formulations elucidate the structure of the discrete operators and are useful when investigating the relationships between operators and their adjoints

finite size scaling of the quasispecies model we use finite size scaling to study the critical behavior of the quasispecies model of molecular evolution in the single sharp peak replication landscape this model exhibits a sharp threshold phenomenon at q q c 1 a where q is the probability of exact replication of a molecule of length l and a is the selective advantage of the master string we investigate the sharpness of the threshold and find that its characteristics persist across a range of q of order l ensuremath 1 about q c furthermore using the data collapsing method we show that the normalized mean hamming distance between the master string and the entire population as well as the properly scaled fluctuations around this mean value follow universal forms in the critical region

an evolutionary version of the random energy model we consider eigen s quasispecies model 1971 of molecular evolution in the case in which the reproduction rates of different molecular species are quenched independent random variables we show by analogy with the random energy model the existence of two phases a neutral phase where no adaptation effects are exhibited and a pathological adapted phase where the population is made of identical optimally adapted molecules and does not evolve

regular article finite difference schemes for u t x α δg δu that inherit energy conservation or dissipation property we propose a new procedure for designing by rote finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations such as the korteweg de vries kdv equation and the cahn hilliard equation the most important feature of our procedure is a rigorous discretization of variational derivatives using summation by parts which implies that the inherited properties are satisfied exactly since the inherited properties are kept even if the time mesh size changes in the time evolution process we can use some appropriate time mesh adaptive methods to obtain numerical solutions through the derived schemes because of these properties the derived schemes are expected to be numerically stable and yield solutions converging to pde solutions and sufficiently flexible to treat the inheritance of the energy conservation and dissipation properties are verified numerically for the kdv equation and the cahn hilliard equation

an efficient time advancing strategy for energy preserving simulations energy conserving numerical methods are widely employed within the broad area of convection dominated systems semi discrete conservation of energy is usually obtained by adopting the so called skew symmetric splitting of the non linear convective term defined as a suitable average of the divergence and advective forms although generally allowing global conservation of kinetic energy it has the drawback of being roughly twice as expensive as standard divergence or advective forms alone in this paper a general theoretical framework has been developed to derive an efficient time advancement strategy in the context of explicit runge kutta schemes the novel technique retains the conservation properties of skew symmetric based discretizations at a reduced computational cost it is found that optimal energy conservation can be achieved by properly constructed runge kutta methods in which only divergence and advective forms for the convective term are used as a consequence a considerable improvement in computational efficiency over existing practices is achieved the overall procedure has proved to be able to produce new schemes with a specified order of accuracy on both solution and energy the effectiveness of the method as well as the asymptotic behavior of the schemes is demonstrated by numerical simulation of burgers equation

approximation of the convective flux in the incompressible navier stokes equations using local boundary value problems abstract we present the spatial discretization of the nonlinear convective flux in the incompressible navier stokes equations using local boundary value problems the finite volume discretization of the incompressible navier stokes equations over staggered grids requires the approximation of the cell face velocity components in the proposed method the cell face velocity components are computed from local boundary value problems with the pressure gradient and the gradient of the transverse flux as source terms the approximation is expressed as the sum of the homogeneous part corresponding to the convection diffusion operator and the inhomogeneous part corresponding to the source terms the homogeneous part of the approximation is shown to be a weighted average of the central and the upwind approximation and thus is first order convergent over coarse grids and second order over finer grids we show that the inhomogeneous part of the approximation effectively removes the numerical diffusion introduced by the homogeneous part the inclusion of the source terms in the local boundary value problem results in a more accurate approximation that shows uniform second order convergence and does not introduce any spurious oscillations

skew symmetric form of convective terms and fully conservative finite difference schemes for variable density low mach number flows the form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by morinishi et al y morinishi t s lund o v vasilyev p moin fully conservative higher order finite difference schemes for incompressible flow j comput phys 124 1998 90 and fully conservative finite difference schemes suitable for shock free unsteady compressible flow simulations are proposed commutable divergence advective and skew symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow these forms are analytically equivalent if the continuity is satisfied and the skew symmetric form is secondary conservative without the aid of the continuity while the divergence form is primary conservative the relations between the present and existing quasi skew symmetric forms are also revealed commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system and they are fully conservative provided that the corresponding discrete continuity is satisfied in addition a semi discrete convection scheme suitable for compact finite difference is presented based on the skew symmetric form the conservation properties of the present schemes are demonstrated numerically in a three dimensional periodic inviscid flow the proposed fully discrete fully conservative second order accurate scheme is also used to perform the dns of compressible isotropic turbulence and the simulation of open cavity flow

the projection method for the incompressible navier stokes equations the pressure near a no slip wall an explicit staggered projection method for the incompressible navier stokes equations with no slip walls is analyzed and used in simulations to address several issues related to the pressure boundary condition required when the continuity equation is replaced by the standard pressure poisson equation ppe 2 p u u f first it is shown that a ppe system supplemented with a neumann pressure boundary condition derived from the momentum equation can be made consistent with the navier stokes equations if it is extended with the requirement that 2 u 0 is zero near the wall and the solution is sufficiently smooth this implies that it is possible to formulate a boundary condition for the standard ppe without the necessity to resort to green s functions which is interesting for theoretical reasons second the equivalence is shown between the staggered projection method and the staggered discretization of above ppe system the derivation of the equivalence sheds light upon the so called ppe paradox and leads to an approximation of the wall value of p n which is not required but implied by the staggered projection method third the near wall regularity of a solution of the navier stokes equations is numerically analyzed by means of direct numerical simulation of turbulent channel flow performed with the staggered projection method from the numerical inspection of all terms of the momentum equation in the near wall region it is concluded that the three components of the momentum equation are satisfied on the wall for t 0 for short times but also in the turbulent regime in the limit t 0 the pressure gradient is observed to converge to the initial pressure gradient in the l 2 norm which confirms a disputed theoretical result in literature even in the maximum norm the pressure gradient appears to converge to the initial pressure gradient the only discontinuities observed in the simulations are the discontinuities of the tangential viscous terms and the time derivatives of the tangential velocities on the wall at t 0 thus the numerical results indicate that the regularity of the solution for turbulent channel flow is stronger than claimed by existing theory

a volume of fluid based simulation method for wave impact problems in this paper some aspects of water impact and green water loading are considered by numerically investigating a dambreak problem and water entry problems the numerical method is based on the navier stokes equations that describe the flow of an incompressible viscous fluid the equations are discretised on a fixed cartesian grid using the finite volume method even though very small cut cells can appear when moving an object through the fixed grid the method is stable the free surface is displaced using the volume of fluid method together with a local height function resulting in a strictly mass conserving method the choice of boundary conditions at the free surface appears to be crucial for the accuracy and robustness of the method for validation results of a dambreak simulation are shown that can be compared with measurements a box has been placed in the flow as a model for a container on the deck of an offshore floater on which forces are calculated the water entry problem has been investigated by dropping wedges with different dead rise angles a cylinder and a cone into calm water with a prescribed velocity the resulting free surface dynamics with the sideways jets has been compared with photographs of experiments also a comparison of slamming coefficients with theory and experimental results has been made finally a drop test with a free falling wedge has been simulated

high order finite difference schemes on non uniform meshes with good conservation properties numerical simulation of turbulent flows dns or les requires numerical methods that are both stable and free of numerical dissipation one way to achieve this is to enforce additional constraints such as discrete conservation of mass momentum and kinetic energy the objective of this work is to generalize the high order schemes of morinishi et al to non uniform meshes while maintaining conservation properties of the schemes as much as possible this generalization is achieved by preserving symmetries of the uniform mesh case the proposed schemes do not simultaneously conserve mass momentum and kinetic energy however depending on the form of the convective term conservation of either momentum or energy in addition to mass can be achieved it is shown that the conservation properties of the generalized schemes are as good as those of the standard second order finite difference scheme on non uniform meshes while the accuracy of the new schemes is definitely superior the predicted conservation properties are demonstrated numerically in inviscid flow simulations

mass momentum and energy conserving mamec discretizations on general grids for the compressible euler and shallow water equations the paper explains a method by which discretizations of the continuity and momentum equations can be designed such that they can be combined with an equation of state into a discrete energy equation the resulting mamec discretizations conserve mass momentum as well as energy although no explicit conservation law for the total energy is present essential ingredients are i discrete convection that leaves the discrete energy invariant and ii discrete consistency between the thermodynamic terms of particular relevance is the way in which finite volume fluxes are related to nodal values the method is an extension of existing methods based on skew symmetry of discrete operators because it allows arbitrary equations of state and a larger class of grids than earlier methods the method is first illustrated with a one dimensional example on a highly stretched staggered grid in which the mamec method calculates qualitatively correct results and a non skew symmetric finite volume method becomes unstable a further example is a two dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid the conservation of mass momentum and energy is checked and losses are found negligible up to machine accuracy

numerically stable formulations of convective terms for turbulent compressible flows abstract a systematic analysis of the discrete conservation properties of non dissipative central difference approximations of the compressible navier stokes equations is reported a generalized splitting of the nonlinear convective terms is considered and energy preserving formulations are fully characterized by deriving a two parameter family of split forms previously developed formulations reported in literature are shown to be particular members of this family novel splittings are introduced and discussed as well furthermore the conservation properties yielded by different choices for the energy equation i e total and internal energy entropy are analyzed thoroughly it is shown that additional preserved quantities can be obtained through a suitable adaptive selection of the split form within the derived family local conservation of primary invariants which is a fundamental property to build high fidelity shock capturing methods is also discussed in the paper numerical tests performed for the taylor green vortex at zero viscosity fully confirm the theoretical findings and show that a careful choice of both the splitting and the energy formulation can provide remarkably robust and accurate results

a gpav based unconditionally energy stable scheme for incompressible flows with outflow open boundaries abstract we present an unconditionally energy stable scheme for approximating the incompressible navier stokes equations on domains with outflow open boundaries the scheme combines the generalized positive auxiliary variable gpav approach and a rotational velocity correction type strategy and the adoption of the auxiliary variable simplifies the numerical treatment for the open boundary conditions the discrete energy stability of the proposed scheme has been proven irrespective of the time step sizes within each time step the scheme entails the computation of two velocity fields and two pressure fields by solving an individual de coupled helmholtz including poisson type equation with a constant pre computable coefficient matrix for each of these field variables the auxiliary variable being a scalar number is given by a well defined explicit formula within a time step which ensures the positivity of its computed values extensive numerical experiments with several flows involving outflow open boundaries in regimes where the backflow instability becomes severe have been presented to test the performance of the proposed method and to demonstrate its stability at large time step sizes

the free distance of fixed convolutional rate 2 4 codes meets the costello bound the long standing question whether the free distance of fixed rate convolutional codes is as good as the costello bound was almost solved by k s zigangirov and j l massey 1987 they proved that this is indeed the case for codes with long branch length and rates 2 c c or 5 it is shown that there exist fixed convolutional codes of rate 2 4 whose free distance d sub free meets the costello bound originally derived for time varying convolutional codes

a new flux splitting scheme a new flux splitting scheme is proposed the scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of roe s solver in the euler and navier stokes solutions carried out in this study the scheme is robust and converges as fast as the roe splitting we propose an appropriately defined cell face advection mach number using values from the two straddling cells via associated characteristic speeds this interface mach number is then used to determine the upwind extrapolation for the convective quantities accordingly the name of the scheme is coined as the advection upstream splitting method ausm we also introduce a new pressure splitting which is shown to behave successfully yielding much smoother results than other existing pressure splittings of particular interest is the supersonic blunt body problem in which the roe scheme gives anomalous solutions the ausm produces correct solutions without difficulty for a wide range of flow conditions as well as grids

improving shock free compressible rans solvers for les on unstructured meshes standard numerical methods used to solve the reynolds averaged navier stokes equations are known to be too dissipative to carry out large eddy simulations since the artificial dissipation they introduce to stabilize the discretization of the convection term usually interacts strongly with the subgrid scale model a possible solution is to resort to non dissipative central schemes unfortunately these schemes are in general unstable a way to reach stability is to select a central scheme that conserves the discrete kinetic energy to that purpose a family of kinetic energy conserving schemes is developed to perform simulations of compressible shock free flows on unstructured grids a direct numerical simulation of the flow past a sphere at a reynolds number of 300 and a large eddy simulation at a reynolds number of 10 000 are performed to validate the methodology

on the properties of discrete spatial filters for cfd the spatial filtering of variables in the context of computational fluid dynamics cfd is a common practice most of the discrete filters used in cfd simulations are locally accurate models of continuous operators however when filters are adaptative i e the filter width is not constant or meshes are irregular discrete filters sometimes break relevant global properties of the continuous models they are based on for example the principle of maxima and minima reduction or conservation are eventually infringed in this paper we analyze the properties of analytic continuous convolution filters and extract those we consider to define filtering then we impose the accomplishment of these properties on explicit discrete filters by means of constraints three filters satisfying the derived conditions are deduced and compared to common differential discrete cfd filters on synthetic fields tests on the developed discrete filters show the fulfillment of the imposed properties in particular the problem of maxima and minima generation is resolved for physically relevant cases the tests are conducted on the basis of the eigenvectors of graph laplacian matrices of meshes thus insight into the relations between filtering and oscillation growth on general meshes is provided further tests on singularity fields and on isentropic vortices have also been conducted to evaluate the performance of filters on basic cfd fields results confirm that imposing the proposed conditions makes discrete filters properties consistent with those of the continuous ones

an advancing front delaunay triangulation algorithm designed for robustness abstract a new algorithm is described for generating an unstructured mesh about an arbitrary two dimensional configuration mesh points are generated automatically by the algorithm in a manner which ensures a smooth variation of elements and the resulting triangulation constitutes the delaunay triangulation of these points the algorithm combines the mathematical elegance and efficiency of delaunay triangulation algorithms with the desirable point placement features boundary integrity and robustness that are traditionally associated with advancing front type mesh generation strategies the method offers increased robustness over previous algorithms in that it cannot fail regardless of the initial boundary point distribution and the prescribed cell size distribution throughout the flow field

high order fluxes for conservative skew symmetric like schemes in structured meshes developing high order non dissipative schemes is an important research task for both steady and unsteady flow computations we take as a starting point the built in de aliasing property of the discretized skew symmetric form for the non linear terms of the navier stokes equations recalled in kravchenko and moin 1 two families of high order locally conservative schemes matching this discretized skew symmetric form are considered and rewritten in terms of telescopic fluxes for both finite difference and finite volume approximations in the context of compressible flows the jameson s scheme 2 is shown to be the second order member of larger families of skew symmetric like centered schemes the fourth order finite volume and finite difference and the sixth order finite difference schemes which belong to this family are provided the proposed schemes are extended to shock capturing schemes either by modifying the jameson s artificial viscosity or by hybriding the centered flux with weno 3 fluxes an adapted interpolation is proposed to extend the use of the proposed schemes to non regular grids several tests are provided showing that the conjectured order is properly recovered even with irregular meshes and that the shock capturing properties allow us to improve the second order results for standard test cases the improvement due to fourth order is then confirmed for the estimation of the growth of two ts waves and three crow instability dimensional unstable modes for both confined and free shear flows the last application concerns the steady computation using the spalart allmaras model of a separated boundary layer it confirms that the use of a high order scheme improves the results even in this type of steady applications

a computational error assessment of central finite volume discretizations in large eddy simulation using a smagorinsky model we present a framework for the computational assessment and comparison of large eddy simulation methods we apply this to large eddy simulation of homogeneous isotropic decaying turbulence using a smagorinsky subgrid model and investigate the combined effect of discretization and model errors at coarse subgrid resolutions we compare four different central finite volume methods these discretization methods arise from the four possible combinations that can be made with a second order and a fourth order central scheme for either the convective and the viscous fluxes by systematically varying the simulation resolution and the smagorinsky coefficient we determine parameter regions for which a desired number of flow properties is simultaneously predicted with approximately minimal error we include both physics based and mathematics based error definitions leading to different error measures designed to emphasize either errors in large or in small scale flow properties it is shown that the evaluation of simulations based on a single physics based error may lead to inaccurate perceptions on quality we demonstrate however that evaluations based on a range of errors yields robust conclusions on accuracy both for physics based and mathematics based errors parameter regions where all considered errors are simultaneously near optimal are referred to as multi objective optimal parameter regions the effects of discretization errors are particularly important at marginal spatial resolution such resolutions reflect local simulation conditions that may also be found in parts of more complex flow simulations under these circumstances the asymptotic error behavior as expressed by the order of the spatial discretization is no longer characteristic for the total dynamic consequences of discretization errors we find that the level of overall simulation errors for a second order central discretization of both the convective and viscous fluxes the 2 2 method and the fully fourth order 4 4 method is equivalent in their respective multi objective optimal regions mixed order methods i e the 2 4 and 4 2 combinations yield errors which are considerably higher

random coding techniques for nonrandom codes this work provides techniques to apply the channel coding theorem and the resulting error exponent which was originally derived for totally random block code ensembles to ensembles of codes with less restrictive randomness demands as an example the random coding technique can even be applied for an ensemble that contains a single code for a specific linear code we get an upper bound for the error probability which equals gallager s 1968 random coding bound up to a factor determined by the maximum ratio between the weight distribution of the code and the expected random weight distribution

a simple approach to discretize the viscous term with spatially varying eddy viscosity a simple approach to discretize the viscous dissipation term in the incompressible navier stokes equations with spatially varying viscosity is presented unlike the case where the viscosity remains constant its discretization may be quite cumbersome especially for high order staggered formulations to circumvent this problem we propose an alternative form of the viscous term whose discretization is straightforward notice that this approach is also suitable for eddy viscosity models for large eddy simulation moreover since it is based on already available operators it can be easily implemented on any structured or unstructured code the supra convergence of the method is numerically shown on both a fourth order cartesian staggered and an unstructured collocated formulation

the dynamic procedure for accuracy improvement of numerical discretizations in fluid mechanics in cfd computations discretization or truncation errors should be small providing an acceptable level of accuracy in this paper an extension is made of the recently proposed les formalism based on sampling operators it is shown that the sampling based dynamic procedure in combination with an appropriate truncation error model can be used as a technique to increase the numerical accuracy of a discretization the technique is resemblant to the well known richardson extrapolation the procedure is tested on a 1d convection diffusion equation and a 2d lid driven cavity at re 400 using a finite difference method promising results are found

scale free networks in evolution abstract in this paper we address the emergence of scale free behavior in a simple evolutionary model we model a growing population that starts from a small number of genotypes and then starts to grow due to an unlimited amount of available resources these genotypes are subjected to the action of natural selection and mutation and increase in number according to their malthusian rates we show that the distribution of links for the genotypes is well described by a scale free distribution this is an evidence that combinatorial optimization processes can yield scale free patterns