fourier chebyshev methods for the incompressible navier stokes equations in infinite domains a fully spectral numerical scheme is presented for the unsteady high reynolds number incompressible navier stokes equations in domains which are infinite or semi infinite in one dimension the domain is not mapped and standard fourier or chebyshev expansions can be used the handling of the infinite domain does not introduce any significant overhead the scheme assumes that the vorticity in the flow is essentially concentrated in a finite region which is represented numerically by standard spectral collocation methods to accommodate the slow exponential decay of the velocities at infinity extra expansion functions are introduced which are handled analytically a detailed error analysis is presented and two applications to direct numerical simulation of turbulent flows are discussed in relation with the numerical performance of the scheme

four decades of studying global linear instability progress and challenges global linear instability theory is concerned with the temporal or spatial development of small amplitude perturbations superposed upon laminar steady or time periodic three dimensional flows which are inhomogeneous in two and periodic in one or all three spatial directions after a brief exposition of the theory some recent advances are reported first results are presented on the implementation of a jacobian free newton krylov time stepping method into a standard finite volume aerodynamic code to obtain global linear instability results in flows of industrial interest second connections are sought between established and more modern approaches for structure identification in flows such as proper orthogonal decomposition and koopman modes analysis dynamic mode decomposition and the possibility to connect solutions of the eigenvalue problem obtained by matrix formation or time stepping with those delivered by dynamic mode decomposition residual algorithm and proper orthogonal decomposition analysis is highlighted in the laminar regime turbulent and three dimensional flows are identified as open areas for future research finally a new stable very high order finite difference method is implemented for the spatial discretization of the operators describing the spatial biglobal eigenvalue problem parabolized stability equation three dimensional analysis and the triglobal eigenvalue problem it is shown that combined with sparse matrix treatment all these problems may now be solved on standard desktop computers

low mach number algorithm for droplet laden turbulent channel flow including phase transition new numerical algorithm for low mach number droplet laden turbulent channel flow with phase transitions the new algorithm eliminates the dependence of the time step on the mach number the results of the new algorithm show close agreement with those of an explicit solver the new algorithm is 200 times faster for ma 0 005 in this study we propose a new numerical algorithm for droplet laden turbulent channel flow with phase transitions at low mach numbers the carrier gas is treated as compressible flow in order to avoid very small time steps at low mach numbers that would arise from stability requirements associated with explicit time stepping we propose a new semi explicit time integration method applied to the low mach number compressible flow equations we perform a perturbation analysis in powers of the mach number of the system of governing equations the obtained decomposition of pressure into a space independent part and a hydrodynamic part permits to apply a special pressure based time integration algorithm for compressible flows at low mach numbers an important feature of the new numerical approach is the independence of the maximum allowed time step on the mach number in this study we validate the new method by comparing it with a fully explicit code for compressible flow at general mach numbers showing a good agreement in all quantities of interest the differences between the results of the two codes are on the order of the square of the mach number caused by the disregard of high order terms in the mach number in the new algorithm the relative difference found for a specific low value of the mach number of 0 05 is on the order of 1 for instantaneous and mean quantities of the two phases we also quantify the efficiency of the new algorithm by comparing the computational time it takes to simulate one time unit with both codes

bayesian inversion of geoelectrical resistivity data summary enormous quantities of geoelectrical data are produced daily and often used for large scale reservoir modelling to interpret these data requires reliable and efficient inversion methods which adequately incorporate prior information and use realistically complex modelling structures we use models based on random coloured polygonal graphs as a powerful and flexible modelling framework for the layered composition of the earth and we contrast our approach with earlier methods based on smooth gaussian fields we demonstrate how the reconstruction algorithm may be efficiently implemented through the use of multigrid metropolis coupled markov chain monte carlo methods and illustrate the method on a set of field data

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

navier stokes solver using green s functions i channel flow and plane couette flow numerical solvers of the incompressible navier stokes equations have reproduced turbulence phenomena such as the law of the wall the dependence of turbulence intensities on the reynolds number and experimentally observed properties of turbulence energy production in this article we begin a sequence of investigations whose eventual aim is to derive and implement numerical solvers that can reach higher reynolds numbers than is currently possible every time step of a navier stokes solver in effect solves a linear boundary value problem the use of green s functions leads to numerical solvers which are highly accurate in resolving the boundary layer which is a source of delicate but exceedingly important physical effects at high reynolds numbers the use of green s functions brings with it a need for careful quadrature rules and a reconsideration of time steppers we derive and implement green s function based solvers for the channel flow and plane couette flow geometries the solvers are validated by reproducing turbulence phenomena in good agreement with earlier simulations and experiment

a sharp interface immersed boundary method for compressible viscous flows an immersed boundary method for computing viscous subsonic compressible flows with complex shaped stationary immersed boundaries is presented the method employs a ghost cell technique for imposing the boundary conditions on the immersed boundaries the current approach leads to a sharp representation of the immersed boundaries a property that is especially useful for flow simulations at high reynolds numbers another unique feature of the method is that it can be applied on cartesian as well as generalized body non conformal curvilinear meshes a mixed second order central difference quick scheme is used which allows a high degree of control over the numerical damping a bilinear interpolation scheme used in conjunction with the ghost cell approach results in second order global as well as local spatial accuracy the solver is parallelized for distributed memory platforms using domain decomposition and message passing interface mpi and salient features of the parallel algorithm are presented the accuracy fidelity and efficiency of the solver are examined by simulating flow past circular cylinders and airfoils and comparing against experimental data and other established results finally we present results from a simulation of wing tip flow at a relatively high reynolds number in order to demonstrate the ability of the solver to model complex non canonical three dimensional flows

accuracy analysis of explicit runge kutta methods applied to the incompressible navier stokes equations this paper investigates the temporal accuracy of the velocity and pressure when explicit runge kutta methods are applied to the incompressible navier stokes equations it is shown that at least up to and including fourth order the velocity attains the classical order of accuracy without further constraints however in case of a time dependent gradient operator which can appear in case of time varying meshes additional order conditions need to be satisfied to ensure the correct order of accuracy furthermore the pressure is only first order accurate unless additional order conditions are satisfied two new methods that lead to a second order accurate pressure are proposed which are applicable to a certain class of three and four stage methods a special case appears when the boundary conditions for the continuity equation are independent of time since in that case the pressure can be computed to the same accuracy as the velocity field without additional cost relevant computations of decaying vortices and of an actuator disk in a time dependent inflow support the analysis and the proposed methods

imaging low frequency and dc electromagnetic fields using a simple linear approximation we consider that all types of electromagnetic measurements represent weighted averages of the subsurface electrical conductivity distribution and that to each type of measurement there corresponds a different weighting function we use this concept for the quantitative interpretation of dc resistivity magnetometric resistivity and low frequency electric and magnetic measurements at low induction numbers in all three cases the corresponding inverse problems are nonlinear because the weighting functions depend on the unknown conductivity distribution we use linear approximations that adapt to the data and do not require reference resistivity values the problem is formulated numerically as a solution of a system of linear equations the unknown conductivity values are obtained by minimizing an objective function that includes the quadratic norm of the residuals as well as the spatial derivatives of the unknowns we also apply constraints through the use of quadratic programming the final product is the flattest model that is compatible with the data under the assumption of the given weighting functions this approximate inversion or imaging technique produces reasonably good results for low and moderate conductivity contrasts we present the results of inverting jointly and individually different data sets using synthetic and field data

on the effect of numerical errors in large eddy simulations of turbulent flows aliased and dealiased numerical simulations of a turbulent channel flow are performed using spectral and finite difference methods analytical and numerical studies show that aliasing errors are more destructive for spectral and high order finite difference calculations than for low order finite difference simulations numerical errors have different effects for different forms of the nonlinear terms in the navier stokes equations for divergence and convective forms spectral methods are energy conserving only if dealiasing is performed for skew symmetric and rotational forms both spectral and finite difference methods are energy conserving even in the presence of aliasing errors it is shown that discrepancies between the results of dealiased spectral and standard nondialiased finite difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences the relative importance of aliasing and truncation errors as compared to subgrid scale model terms in large eddy simulations is analyzed and discussed for low order finite difference simulations truncation errors can exceed the magnitude of the subgrid scale term

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

modified immersed boundary method for flows over randomly rough surfaces abstract many phenomena ranging from biology to electronics involve flow over rough or irregular surfaces we treat such surfaces as random fields and use an immersed boundary method ibm with discrete random forcing to solve resulting stochastic flow problems our approach relies on the uhlmann formulation of the fluid solid interaction force computational savings stem from the modification of the time advancement scheme that obviates the need to solve the poisson equation for pressure at each sub step we start by testing the proposed algorithm on two classical benchmark problems the first deals with the wannier problem of stokesian flow around a cylinder in the vicinity of a moving plate the second problem considers steady state and transient flows over a stationary circular cylinder our simulation results show that our algorithm achieves second order temporal accuracy it is faster than the original ibm while yielding consistent estimates of such quantities of interest as the drag and lift coefficients the length of a recirculation zone in a cylinder s wake and the strouhal number then we use the proposed ibm algorithm to model flow over cylinders whose surface is either deterministically corrugated or randomly rough

an adaptive implicit explicit scheme for the dns and les of compressible flows on unstructured grids an adaptive implicit explicit scheme for direct numerical simulation dns and large eddy simulation les of compressible turbulent flows on unstructured grids is developed the method uses a node based finite volume discretization with summation by parts sbp property which in conjunction with simultaneous approximation terms sat for imposing boundary conditions leads to a linearly stable semi discrete scheme the solution is marched in time using an implicit explicit runge kutta imex rk time advancement scheme a novel adaptive algorithm for splitting the system into implicit and explicit sets is developed the method is validated using several canonical laminar and turbulent flows load balance for the new scheme is achieved by a dual constraint domain decomposition algorithm the scalability and computational efficiency of the method is investigated and memory savings compared with a fully implicit method is demonstrated a notable reduction of computational costs compared to both fully implicit and fully explicit schemes is observed

a third order multistep time discretization for a chebyshev tau spectral method a time discretization scheme based on the third order backward difference formula has been embedded into a chebyshev tau spectral method for the navier stokes equations the time discretization is a variant of the second order backward scheme proposed by krasnov et al 2008 3 high resolution direct numerical simulations of turbulent incompressible channel flow have been performed to compare the backward scheme to the runge kutta scheme proposed by spalart et al 1991 2 it is shown that the runge kutta scheme leads to a poor convergence of some third order spatial derivatives in the direct vicinity of the wall derivatives that represent the diffusion of wall tangential vorticity the convergence at the wall is shown to be significantly improved if the backward scheme is applied

using wavelet packet denoising and anfis networks based on cosfla optimization for electrical resistivity imaging inversion abstract electrical resistivity imaging eri inversion is a complicated non linear inversion problem which is high dimensional and non convex using traditional neural networks to solve the eri inversion problem has an over fitting phenomenon and easily falls into local minima moreover the artificial neural network ann model is a black box its relationships between the inputs and outputs are not easy to interpret in order to solve these problems a wavelet packet denoising wpd procedure and an improved adaptive neuro fuzzy inference system anfis based on cauchy oscillation shuffled frog leaping algorithm cosfla are proposed in this paper the wavelet packet denoising methodology is based on soft thresholding and shannon entropy using a db10 wavelet which is applied to remove the noise component from the measured apparent resistivity data meanwhile cosfla is introduced for updating the premise parameters of the anfis to improve the learning ability and prediction accuracy of the algorithm the development of the proposed method and the total inversion process are also presented the inversion of the synthetic and field examples are provided to demonstrate the feasibility and validity of the proposed method additionally the introduced method is transparent and its if then rules are easy to understand and interpret

an extension of dickstein s small lambda theorem for finite time blowup abstract in this paper we prove for 1 p 1 1 n 1 l 1 r n with r n 0 and c 0 r n w 1 1 r n with r n 0 such that j that there exists 0 such that the solution u of the equation u t u u p 1 u with u 0 blows up in finite time for all 0 this extends a similar result of dickstein who treated the case r n 0 and 1 p 1 2 n

spectrally accurate immersed boundary conditions method for three dimensional flows a three dimensional spectrally accurate algorithm based on the immersed boundary conditions ibc concept has been developed for the analysis of flows in channels bounded by rough boundaries the algorithm is based on the velocityvorticity formulation and uses a fixed computational domain with the flow domain immersed in its interior the geometry of the boundaries is expressed in terms of double fourier expansions and boundary conditions enter the algorithm in the form of constraints the spatial discretization uses fourier expansions in the stream wise and span wise directions and chebyshev expansions in the wall normal direction the algorithm can use either the fixed flow rate constraint or the fixed pressure gradient constraint a direct implementation of the former constraint is described an efficient solver which takes advantage of the structure of the coefficient matrix has been developed it is demonstrated that the applicability of the algorithm can be extended to more extreme geometries using the over determined formulation various tests confirm the spectral accuracy of the algorithm

a fourier hermite pseudospectral method for penetrative convection a fourier hermite pseudospectral method is developed to study numerically the three dimensional penetrative convection problem under the boussinesq approximation an s shaped temperature profile in the absence of motion is prescribed in the vertical direction all variables are expanded in terms of fourier hermite basis functions the hermite functions are scaled to adjust the length of the computational domain in the vertical a semi implicit scheme is used for time marching with the third order adam bashforth and crank nicholson scheme for the nonlinear and linear terms respectively an implementation of the numerical method on a parallel computer is also described numerical simulation results of resolution 643are presented for low to moderate rayleigh numbers with a prandtl number of unity the highly stable outer regions are seen to act as effective lids and all penetrative flow are contained within the computational box variances heat fluxes and their budgets are reported for several rayleigh numbers to demonstrate the efficacy of the numerical method

time dependent singularities in semilinear parabolic equations existence of solutions abstract we study the existence of solutions of the semilinear parabolic equation t u u u p in d r n i here n 2 p 1 n 2 p n and i r is an open interval it is assumed that d r n i is supported on t t r n 1 t i for some c 1 2 i r n and is given by i t t d t where is a radon measure on i satisfying a b b a a b i for some positive function in the case where i is bounded we give conditions on the behavior of near 0 for the existence and nonexistence of solutions the existence for i r is also shown under additional conditions on p and the behavior of near moreover the singularity of solutions at x t is examined

an efficient method for temporal integration of the navier stokes equations in confined axisymmetric geometries a method for temporal integration of the navier stokes equations written in cylindrical coordinates is described the objective is to avoid the severe time step limitation usually encountered in confined axisymmetric geometries e g pipe flow caused by a fine azimuthal grid spacing around the centerline and the desire to refine the grid in the radial direction near walls avoiding severe time step limitations usually involves treating all terms with derivatives in the radial and azimuthal directions with an implicit time integration scheme however this leads to a set of coupled nonlinear equations which generally require complex and costly solution procedures the scheme described in this paper decomposes the computational domain into two regions within each region only the derivatives in one coordinate direction is treated implicitly conditions at the interface between the regions are determined to maintain the overall temporal accuracy of the basic time integration schemes results from a direct numerical simulation dns of turbulent pipe flow are validated against computational and experimental results from the literature it is demonstrated that this new scheme allows for larger time steps than other schemes leading to significant cpu savings

eigenmodes of a counter rotating vortex dipole highly resolved solutions of the two dimensional incompressible navier stokes and continuity equations describing the evolution of a counter rotating pair of vortices have been obtained accurately and efficiently by spectral collocation methods and an eigenvalue decomposition algorithm such solutions have formed the basic state for subsequent three dimensional biglobal eigenvalue problem linear instability analyses which monitor the modal response of these vortical systems to small amplitude perturbations periodic along the homogeneous axial spatial direction without the need to invoke an assumption of azimuthal spatial homogeneity a finite element methodology gonzalez l m theofilis v and gomez blanco r finite element numerical methods for viscous incompressible biglobal linear instability analysis on unstructured meshes aiaa journal vol 45 no 4 2007 pp 840 855 has been adapted to study the instability of vortical flows and has been validated on the batchelor vortex mayer e w and powell k g viscous and inviscid instabilities of a trailing vortex journal of fluid mechanics vol 245 1992 pp 91 114 subsequently the instability of the counter rotating dipole has been analyzed aspects monitored have been the dependence of the results on the reynolds number the value of the nonzero axial velocity considered and the time at which the quasi steady basic flow has been monitored essential to the success of the analysis has been the appropriate design of a calculation mesh as well as exploitation of the symmetries of the basic state the spatial structure of the amplitude functions of all unstable eigenmodes reflects the inhomogeneity of the basic state in the azimuthal spatial direction thus providing a posteriori justification for the use of the biglobal eigenvalue problem concept

the use and misuse of apparent resistivity in electromagnetic methods problems and misunderstandings arise with the concept of apparent resistivity when the analogy between an apparent resistivity computed from geophysical observations and the true resistivity structure of the subsurface is drawn too tightly several definitions of apparent resistivity are available for use in electromagnetic methods however those most commonly used do not always exhibit the best behavior many of the features of the apparent resistivity curve which have been interpreted as physically significant with one definition disappear when alternative definitions are used it is misleading to compare the detection or resolution capabilities of different field systems or configurations solely on the basis of the apparent resistivity curve for the in loop transient electromagnetic tem method apparent resistivity computed from the magnetic field response displays much better behavior than that computed from the induced voltage response a comparison of exact and asymptotic formulas for the te

the optimization of convergence for chebyshev polynomial methods in an unbounded domain by using the method of steepest descent i have compared the suitability of three different methods for solving problems in a semi infinite or infinite domain using chebyshev polynomials exponential mappings are uniformyly bad domain truncation and algebraic mapping both work well but each is superior for a different category of problems when the solution is an entire function then domain truncation is best it is always simpler to apply than algebraic mapping and always at least as accurate much more accurate for functions which decay very rapidly for singular functions on the other hand algebraic mapping is better because it is less sensitive to the mapping scale factor l permitting a better compromise in resolving both the singularity and the exponential decay for both types of problems i give simple explicit estimates of both the optimum choise of domain size or mapping factor and of the attainable accuracy for the model entire function exp azk on a semi infinite interval 0 the optimum domain size is l 0 896 na 1k and the smallest attainable error is roughly e n 0 896 k where n is the number of chebyshev polynomals used similar formulas for singular functions handled via algebraic mapping are given in 3 41 to 3 45 below

a model for the simulation of turbulent boundary layers in an incompressible stratified flow a model with several original physical and numerical features has been developed for direct numerical and large eddy simulations of a turbulent boundary layer in a stratified fluid the large scale flow for which the model was developed involves internal waves reflecting from a sloping boundary in the model the internal waves are generated by a new technique that forces monochromatic waves at specified wavelengths and frequencies a new analytic solution has been obtained representative of the forcing conditions in the model time discretization is based upon the projection method incorporating a third order adams bashforth scheme with variable time steps and spatial discretization employs fourth order compact differencing techniques on a variable grid that increases resolution close to the boundary the model is periodic in two dimensions and in the third dimension employs an open boundary and a solid sloping surface the pressure field is determined using a fast direct solution method of fourth order accuracy the model includes flow analysis aids such as tracking lagrangian particles and advected scalar quantities flow measurements are made of the integrated kinetic and potential energy balances local dissipation rates and the energy spectra the utility of the model is examined in a number of test problems it appears that the model is well suited for simulations of transitioning and turbulent boundary layers

semi implicit runge kutta schemes development and application to compressible channel flow time stepconstraintdueto thefine meshnear thewall the explicitsubschemeis asix stage fourth order low storage runge kutta scheme based on analysis in fourier space and results obtained for propagation test cases the semiimplicitschemesareshowntobeoforder3and forwavesdiscretizedbyanumberofpointsperperiodbetween4and 16 tobeasaccurateas ormoreaccuratethan thestandardexplicitfourth orderrunge kuttaalgorithmintermsof dissipationanddispersion thelarge eddysimulationofacompressibleturbulentchannelflowatafrictionreynolds numberof360andamachnumberof0 1isthencarriedoutwithoneoftheproposedalgorithms thecomputational time is reduced by a factor 1 33 with respect to a large eddy simulation using the explicit subscheme in all directions wall pressure and velocity spectra from the large eddy simulation are presented to give insights into the flow turbulent structures in particular wave number frequency spectra are calculated acoustic components appear to be identified in these spectra

spectral methods for the navier stokes equations with one infinite and two periodic directions abstract two numerical methods were designed to solve the time dependent three dimensional incompressible navier stokes equations in boundary layers method a semi infinite domain and mixing layers or wakes method b fully infinite domain their originality lies in the use of rapidly decaying spectral basis functions to approximate the vertical dependence of the solutions combined with one method a or two method b slowly decaying extra functions for each wave vector that exactly represent the irrotational component of the solution at large distances both methods eliminate the pressure term as part of the formulation thus avoiding fractional step time integration they yield rapid convergence and are free of spurious modes in the orr sommerfeld spectra they are also efficient although the operation count is of order n 2 n is the number of modes in the infinite direction these methods have been used for extensive direct numerical simulations of transition and turbulence a new time integration scheme with low storage requirements and good stability properties is also described

a second order accurate immersed boundary method for fully resolved simulations of particle laden flows an immersed boundary method ibm with second order spatial accuracy is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles the method is based on the computationally efficient direct forcing method of uhlmann m uhlmann an immersed boundary method with direct forcing for simulation of particulate flows j comput phys 209 2005 448 476 that is embedded in a finite volume pressure correction method the ibm consists of two grids a fixed uniform eulerian grid for the fluid phase and a uniform lagrangian grid attached to and moving with the particles a regularized delta function is used to communicate between the two grids and proved to be effective in suppressing grid locking without significant loss of efficiency the original method is improved by 1 a better approximation of the no slip no penetration ns np condition on the surface of the particles by a multidirect forcing scheme 2 a correction for the excess in the effective particle diameter by a slight retraction of the lagrangian grid from the surface towards the interior of the particles with a fraction of the eulerian grid spacing and 3 an enhancement of the numerical stability for particle fluid mass density ratios near unity by a direct account of the inertia of the fluid contained within the particles the new ibm contains two new parameters the number of iterations n s of the multidirect forcing scheme and the retraction distance r d the effect of n s and r d on the accuracy is investigated for five different flows the results show that r d has a strong influence on the effective particle diameter and little influence on the error in the ns np condition while exactly the opposite holds for n s a novel finding of this study is the demonstration that r d has a strong influence on the order of grid convergence it is found that for spheres the choice of r d 0 3 dx yields second order accuracy compared to first order accuracy of the original method that corresponds to r d 0 finally n s 2 appears optimal for reducing the error in the ns np condition and maintaining the computational efficiency of the method

discrete orthogonal function expansions for non uniform grids using the fast fourier transform abstract discrete orthogonal function expansions are obtained for non uniformly spaced data by combined use of mapping functions and the fast fourier transform the result yields alias free differentiation and integration operators the method is applicable to periodic zero or zero derivative boundary conditions or combinations thereof truncation is required to avoid aliasing and or singularity but the truncation error is explicit quantitatively expressible and generally small this approach is demonstrated in an infinite physical domain with application to linear convection and diffusion the resulting errors are orders of magnitude smaller than those generated by standard finite difference methods difficulties arising from image fields are an important phenomena the method of differentiation as well as the boundary conditions imply artificial image fields a vortex pairing problem is presented which shows that image flows can totally alter the solution the new scheme avoids this undesirable effect by keeping image flows infinitely far away

high order accurate solution of the incompressible navier stokes equations on massively parallel computers the emergence of petascale supercomputers requires us to develop today s simulation codes for incompressible flows by codes which are using numerical schemes and methods that are better able to exploit the offered computational power in that spirit we present a massively parallel high order navier stokes solver for large incompressible flow problems in three dimensions the governing equations are discretized with finite differences in space and a semi implicit time integration scheme this discretization leads to a large linear system of equations which is solved with a cascade of iterative solvers the iterative solver for the pressure uses a highly efficient commutation based preconditioner which is robust with respect to grid stretching the efficiency of the implementation is further enhanced by carefully setting the adaptive termination criteria for the different iterative solvers the computational work is distributed to different processing units by a geometric data decomposition in all three dimensions this decomposition scheme ensures a low communication overhead and excellent scaling capabilities the discretization is thoroughly validated first we verify the convergence orders of the spatial and temporal discretizations for a forced channel flow second we analyze the iterative solution technique by investigating the absolute accuracy of the implementation with respect to the different termination criteria third orr sommerfeld and squire eigenmodes for plane poiseuille flow are simulated and compared to analytical results fourth the practical applicability of the implementation is tested for transitional and turbulent channel flow the results are compared to solutions from a pseudospectral solver subsequently the performance of the commutation based preconditioner for the pressure iteration is demonstrated finally the excellent parallel scalability of the proposed method is demonstrated with a weak and a strong scaling test on up to o 10 4 processing units and o 10 1 1 grid points

a spectral b spline method for the navier stokes equations in unbounded domains the numerical method presented in this paper aims at solving the incompressible navier stokes equations in unbounded domains the problem is formulated in cylindrical coordinates and the method is based on a galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint more specifically the divergence free basis vector functions are constructed with fourier expansions in the and z directions while mapped b splines are used in the semi infinite radial direction special care has been taken to account for the particular analytical behaviors at both end points r 0 and r a modal reduction algorithm has also been implemented in the azimuthal direction allowing for a relaxation of the cfl constraint on the timestep size and a possibly significant reduction of the number of dof the time marching is carried out using a mixed quasi third order scheme besides the advantages of a divergence free formulation and a quasi spectral convergence the local character of the b splines allows for a great flexibility in node positioning while keeping narrow bandwidth matrices numerical tests show that the present method compares advantageously with other similar methodologies using purely global expansions

an automatic technique for presentation of coincident loop impulse response transient electromagnetic data coincident loop tem sounding data are often presented by plotting the half space apparent conductivity as a function of delay time a new algorithm generates an improved presentation that plots the apparent conductivity as a function of depth the resulting data may be further processed to sharpen or spike the smoothly varying apparent conductivity depth curves in an attempt to better represent the rapid changes in conductivity that often exist in the earth the algorithm described involves an approximation but is simple easy to use and computationally efficient a layered conductivity structure is assumed so the algorithm is best for areas where the geology is approximately horizontal however the algorithm can also be used to identify anomalous features that are not infinite horizontal layers the spiked conductivity models derived from synthetic data are consistent with the original layered earth models and show a greater resolution than the apparent conductivity depth curves and sometimes ampl

global existence for the nonlinear heat equation in the fujita subcritical case with initial value having zero mean value abstract in this paper we prove for 1 p 1 2 n k where k is an integer in 1 n the existence of an initial value odd with respect to the k first coordinates and with r n x 1 x k d x 1 d x n 0 such that the resulting solution of u t u u p 1 u is global in the case k 1 and 1 p 1 1 n 1 it is known that the solution u with the initial value u 0 blows up in finite time if 0 either sufficiently small or sufficiently large the result in this paper extends a similar result of cazenave dickstein and weissler in the case k 0 i e with r n 0 and 1 p 1 2 n

incompressibility and no slip boundaries in the chebyshev tau approximation i present a minor but important correction to kleiser and schumann s influence matrix solution for numerical simulation of 3d time dependent incompressible flow between no slip plane boundaries l kleiser and u schumann in proc 3rd gamm conf numerical methods in fluid mechanics edited by e h hirschel vieweg braunschweig 1980 p 165 the solution technique i present is for the most part identical to kleiser and schumann s the only noteworthy difference being my treatment of the truncation or tau errors though this improvement appears to be but a slight modification to their original algorithm the error encountered when attempting to satisfy the incompressibility constraint is reduced dramatically by a factor of 1011 producing velocity fields which are divergence free to within machine precision

highly energy conservative finite difference method for the cylindrical coordinate system a highly energy conservative second order accurate finite difference method for the cylindrical coordinate system is developed it is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used this argument holds not only for an unequally spaced mesh but also for an equally spaced mesh on cylindrical coordinates but not on cartesian coordinates numerical tests are undertaken for an inviscid flow with various schemes and it turns out that the proposed scheme offers a superior energy conservation property and greater stability than the intuitive and previously proposed methods for both equally spaced and unequally spaced meshes

numerical method for incompressible vortical flows with two unbounded directions a new efficient and accurate method has been developed for computing unsteady incompressible viscous flows in a domain where two dimensions are unbounded the third dimension is periodic and the vorticity is rapidly decaying in the unbounded directions we use the term unbounded to mean doubly infinite no boundaries of any kind this is an extension of the methods described by others for flows with two periodic and one unbounded direction where the irrotational velocities outside the vortical domain are treated analytically the new method is shown to be both accurate and efficient the method presented here has finite but arbitrarily high order formal accuracy and incurs substantial additional cost for a given mesh however this increased cost is more than offset by the reduction in the number of mesh points required for a given accuracy the result is that for accurate computations the present method can be orders of magnitude more efficient than others currently in use this paper presents the method discusses implementation issues validates its accuracy and presents sample calculations

an improved immersed boundary method with direct forcing for the simulation of particle laden flows an efficient approach for the simulation of finite size particles with interface resolution was presented by uhlmann m uhlmann an immersed boundary method with direct forcing for the simulation of particulate flows j comput phys 209 2005 448 476 the present paper proposes several enhancements of this method which considerably improve the results and extend the range of applicability an important step is a simple low cost iterative procedure for the euler lagrange coupling yielding a substantially better imposition of boundary conditions at the interface even for large time steps furthermore it is known that the basic method is restricted to ratios of particle density and fluid density larger than some critical value above 1 hence excluding for example non buoyant particles this can be remedied by an efficient integration step for the artificial flow field inside the particles to extend the accessible density range down to 0 3 this paper also shows that the basic scheme is inconsistent when moving surfaces are allowed to approach closer than twice the step size a remedy is developed based on excluding from the force computation all surface markers whose stencil overlaps with the stencil of a marker located on the surface of a collision partner the resulting algorithm is throughly validated and is demonstrated to substantially improve upon the original method

a new high order method for the simulation of incompressible wall bounded turbulent flows a new method to perform direct numerical simulations of wall bounded flows has been developed and implemented the method uses high order compact finite differences in wall normal for channel flow or radial direction for pipe flow on a collocated grid which gives high accuracy results without the effectfof filtering caused by frequent interpolation as required on a staggered grid the use of compact finite differences means that extreme clustering near the wall leading to small time steps in high reynolds number simulations is avoided the influence matrix method is used to ensure a completely divergence freesolution and all systems of equations are solved in banded form which ensures an effcient solution procedure with low requirements for data storage the method is unique in the sense that exactly divergence free solutions on collocated meshes are calculated using arbitrary dffierence matrices the code is validated for two flow cases i e turbulent channel and turbulent pipe flow at relatively low reynolds number all tests show excellent agreement with analytical and existing results confirming the accuracy and robustness ofthe method the next step is to eciently parallelise the code so that high reynolds number simulations at high resolution can be performed we furthermore investigated rare events occurring in the near wall region of turbulent wall bounded flows we find that negative streamwise velocities and extreme wall normal velocity uctuations are found rarely on the order of 0 01 and that they occur more frequently at higher reynolds number these events are caused by strong vortices lying further away from the wall and it appears that these events are universal for wall bounded flows

nonlinear integral equations for electromagnetic inverse problems the scaling properties of maxwell s equations allow the existence of simple yet general nonlinear integral equations for electrical conductivity these equations were developed in an attempt to reduce the generality of linearization to the exclusive scope of electromagnetic problems the reduction is achieved when the principle of similitude for quasi static fields is imposed on linearized forms of the field equations the combination leads to exact integral relations which represent a unifying framework for the general electromagnetic inverse problem the equations are of the same form in both time and frequency domains and hold for all observations that scale as electric and magnetic fields do direct current resistivity and magnetometric resistivity methods are considered as special cases the kernel functions of the integral equations are closely related through a normalization factor to the frechet kernels of the conventional equations obtained by linearization accordingly the sensitivity functio

blowup stability of solutions of the nonlinear heat equation with a large life span abstract we study the cauchy problem for the nonlinear heat equation u t u u p 1 u in r n the initial data is of the form u 0 where c 0 r n is fixed and 0 we first take 1 p p f where p f is the fujita critical exponent and c 0 r n l 1 r n with nonzero mean we show that u t blows up for small extending the h fujita blowup result for sign changing solutions next we consider 1 p p s where p s is the sobolev critical exponent and x decaying as x at infinity where p 1 2 we also prove that u t blows up when is small extending a result of t lee and w ni for both cases the solution enjoys some stable blowup properties for example there is single point blowup even if is not radial

least squares deconvolution of apparent resistivity pseudosections a fast technique for the inversion of data from resistivity tomography surveys has been developed this technique is based on the smoothness constrained least squares method and it produces a 2 d subsurface model that is free of distortions in the apparent resistivity pseudosection caused by the electrode array geometry used a homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically tests with a variety of models and data from field surveys show that this technique is insensitive to random noise provided a sufficiently large damping factor is used and that it can resolve structures that cause overlapping anomalies in the pseudosection on a 33 mhz 80486dx microcomputer it takes about 5 s to process a single data set

a spectral numerical method for the navier stokes equations with applications to taylor couette flow a new spectral method for solving the incompressible navier stokes equations in a plane channel and between concentric cylinders is presented the method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step in addition the number of dependent variables is reduced resulting in a reduction in computer memory requirements several test problems have been computed for the channel flow and for flow between concentric cylinders including taylor couette flow with axisymmetric taylor vortices and wavy vortices in all cases agreement with available experimental and theoretical results is very good

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

a finite difference scheme for three dimensional incompressible flows in cylindrical coordinates a finite difference scheme for the direct simulation of the incompressible time dependent three dimensional navier stokes equations in cylindrical coordinates is presented the equations in primitive variables vr v vzandp are solved by a fractional step method together with an approximate factorization technique cylindrical coordinates are singular at the axis the introduction of the radial fluxqr r vron a staggered grid simplifies the treatment of the region atr 0 the method is tested by comparing the evolution of a free vortex ring and its collision with a wall with the theory experiments and other numerical results the formation of a tripolar vortex where the highest vorticity is atr 0 is also considered finally to emphasize the accurate treatment near the axis the motion of a lamb dipole crossing the origin is simulated

finite difference method for incompressible navier stokes equations in arbitrary orthogonal curvilinear coordinates a finite difference method for solving three dimensional time dependent incompressible navier stokes equations in arbitrary curvilinear orthogonal coordinates is presented the method is oriented on turbulent flow simulations and consists of a second order central difference approximation in space and a third order semi implicit runge kutta scheme for time advancement spatial discretization retains some important properties of the navier stokes equations including energy conservation by the nonlinear and pressure gradient terms numerical tests cover cartesian cylindrical polar spherical cylindrical elliptic and cylindrical bipolar coordinate systems both laminar and turbulent flows are considered demonstrating reasonable accuracy and stability of the method

a finite element method with mesh adaptivity for computing vortex states in fast rotating bose einstein condensates numerical computations of stationary states of fast rotating bose einstein condensates require high spatial resolution due to the presence of a large number of quantized vortices in this paper we propose a low order finite element method with mesh adaptivity by metric control as an alternative approach to the commonly used high order finite difference or spectral approximation methods the mesh adaptivity is used with two different numerical algorithms to compute stationary vortex states an imaginary time propagation method and a sobolev gradient descent method we first address the basic issue of the choice of the variable used to compute new metrics for the mesh adaptivity and show that refinement using simultaneously the real and imaginary part of the solution is successful mesh refinement using only the modulus of the solution as adaptivity variable fails for complicated test cases then we suggest an optimized algorithm for adapting the mesh during the evolution of the solution towards the equilibrium state considerable computational time saving is obtained compared to uniform mesh computations the new method is applied to compute difficult cases relevant for physical experiments large nonlinear interaction constant and high rotation rates

occam s inversion a practical algorithm for generating smooth models from electromagnetic sounding data the inversion of electromagnetic sounding data does not yield a unique solution but inevitably a single model to interpret the observations is sought we recommend that this model be as simple or smooth as possible in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models to obtain smooth models the nonlinear forward problem is linearized about a starting model in the usual way but it is then solved explicitly for the desired model rather than for a model correction by parameterizing the model in terms of its first or second derivative with depth the minimum norm solution yields the smoothest possible model rather than fitting the experimental data as well as possible which maximizes the roughness of the model the smoothest model which fits the data to within an expected tolerance is sought a practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models resulting in a stable and rapidly convergent algorithm the inversion of both magnetotelluric and schlumberger sounding field data and a joint magnetotelluric resistivity inversion demonstrate the method and show it to have practical application

near wall les closure based on one dimensional turbulence modeling a novel near wall les closure model is developed based on a revised form of the one dimensional turbulence odt model of kerstein and is tested by performing les calculations of turbulent channel flow at reynolds numbers based on friction velocity ranging from 395 to 10 000 in contrast to previous models which invoke reynolds averaging near wall velocity fluctuations and turbulent transport are simulated down to the smallest scales and can be compared directly to dns data thus the approach provides more than just a boundary condition rather it is itself a complete although simplified model for the wall normal profiles of velocity within the near wall region les odt coupling is bi directional and occurs both through the direct calculation of the subgrid turbulent stress by temporally and spatially filtering the odt resolved momentum fluxes up scale coupling and through the les resolved pressure and velocities impacting the odt behavior down scale coupling the formulation involves finely resolved odt lines that are embedded within each wall adjacent les cell denoted the inner region les cells that are within approximately one les filter width of the inner region belong to an overlap region where both odt and les modeling is active all other cells are treated using a standard les approach although more expensive than simpler models the cost of the model relative to the les portion of the simulation scales favorably with problem size leading to computationally affordable simulations even at relatively high reynolds numbers

a spectral method for unbounded domains a spectral method for an unbounded domain is presented rational basis functions which are algebraically mapped legendre functions are used for expansion in the radial direction of polar coordinates r or r z they satisfy the pole condition exactly at the coordinate singularity and their behavior asr is suitable for expanding smooth functions which decay algebraically or exponentially asr the method is not stiff when it is applied to initial value problems despite the presence of the coordinate singularity solenoidal vector fields are treated efficiently by the toroidal and poloidal decomposition which reduces the number of dependent variables from 3 to 2 examples include the computation of vortex dynamics in two and three dimensions

a sparse mesh for compact finite difference fourier solvers with radius dependent spectral resolution in circular domains this paper presents a new method for the resolution of elliptic and parabolic equations in circular domains it can be trivially extended to cylindrical domains the algorithm uses a mixed fourier compact finite difference method the main advantage of the method is achieved by a new concept of mesh the topology of the new grid keeps constant the aspect ratio of the cells avoiding the typical clustering for radial structured meshes at the center the reduction of the number of nodes has as a consequence the reduction in memory consumption in the case of fluid mechanics problems this technique also increases the time step for a constant courant number several examples are given in the paper which show the potential of the method

global existence and blowup for sign changing solutions of the nonlinear heat equation abstract in this paper given 0 2 n we prove the existence of a function with the following properties the solution of the equation u t u u u on r n with the initial condition u 0 is global on the other hand the solution with the initial condition u 0 blows up in finite time if 0 is either sufficiently small or sufficiently large