development of high order taylor galerkin schemes for les in this paper we describe the implementation and development of a new taylor galerkin finite element scheme within an unstructured hybrid parallel solver the scheme has been specifically conceived for unsteady les it is third order in space and time and has a low dissipative error minimal additional cpu costs are achieved by using a new approximation of the finite element integrals and a simple iterative method for the approximate inversion of the modified mass matrix basic convective tests are carried out in 2 and 3 dimensions for arbitrary elements numerical estimates of the order of convergence are presented on regular and perturbed grids finally test cases that are relevant to les are carried out and these clearly demonstrate the important improvements that our new scheme offers relative to a selection of existing methods

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

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

applications of the numerical inversion of the laplace transform to unsteady problems of the third grade fluid abstract in this article we have effectively used the numerical inversion of laplace transform to study some time dependent problems of the third grade fluid to do so we have considered three different types of unsteady flows of the third grade fluid namely a unsteady flow over a flat rigid plate with porous medium b unsteady mhd flow in a porous medium c unsteady mhd flow in a non porous space with hall currents the solution to the governing equation in each case is obtained by using the standard laplace transform however to transform the obtained solutions from laplace space back to the original space we have used the numerical inversion of the laplace transform graphical results for each case have been presented to show the effects of different parameters involved and to show how the fluid flow evolves with time

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

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

on the computation of multi dimensional solution manifolds of parametrized equations a new algorithm is presented for computing vertices of a simplicial triangulation of thep dimensional solution manifold of a parametrized equationf x 0 wheref is a nonlinear mapping fromr n tor m p n m 1 an essential part of the method is a constructive algorithm for computing moving frames on the manifold that is of orthonormal bases of the tangent spaces that vary smoothly with their points of contact the triangulation algorithm uses these bases together with a chord form of the gauss newton process as corrector to compute the desired vertices the jacobian matrix of the mapping is not required at all the vertices but only at the centers of certain local triangulation patches several numerical examples show that the method is very efficient in computing triangulations even around singularities such as limit points and bifurcation points this opens up new possibilities for determining the form and special features of such solution manifolds

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

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

application of the entropically damped artificial compressibility model to direct numerical simulation of turbulent channel flow abstract the feasibility of the entropically damped artificial compressibility edac model for simulation of wall bounded turbulence is examined a favourable feature of edac is the purely parabolic type of governing equations resulting from the introduction of a damping term to the pressure evolution equation this significantly reduces noise in the velocity divergence field when central schemes are applied for the spatial discretisation the method of lines is used for the solution of the edac equations a conservative finite difference method of purely 2nd and mixed 4th 2nd order is applied the explicit 4th order six stage low storage runge kutta method is used for time advancement as expected the mixed scheme is superior to the 2nd order one in terms of both accuracy and computational efficiency for the first time the edac model is assessed for the direct numerical simulation of wall bounded turbulent flow requiring a non uniform mesh as a particular test case we have chosen the channel flow at the friction reynolds numbers r e 180 and 395 a very good agreement with the reference data is obtained as documented by the chosen one point velocity statistics the mean and r m s profiles and the budgets of the reynolds stresses the use of the explicit time discretisation and local rather than compact spatial schemes results in easily and efficiently parallelisable solution algorithm we achieved very high computational performance on a desktop computer when solving the edac equations using a code dedicated for the graphics processing unit gpu the aspects of the gpu implementation are discussed

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

short note turbulent channel flow simulations in convecting reference frames we perform finite difference numerical simulations of turbulent channel flow in stationary and moving reference frames the flow statistics computed in the stationary frame exhibit significant discrepancies with respect to reference spectral data in terms of energy spectra and convection velocity of disturbances especially in the near wall region on the other hand simulations performed in a reference frame moving with the bulk flow velocity suffer from this shortcoming to a much lesser extent we propose an explanation of these observations by assuming the scalar burgers equation as working model the analysis highlights the lack of galilean invariance of finite difference schemes which exhibit a leading dispersive error in the presence of bulk advection the numerically computed energy spectra exhibit the same features as the channel spectra supporting the notion that dispersive effects are responsible for the blockage of the mechanism of energy cascade to high wavenumbers

the influence of slip condition on thin film flow of a fourth grade fluid by the homotopy analysis method this paper provides an investigation regarding slip effects on thin film flow of a fourth grade fluid down a vertical cylinder the nonlinear problem that arises is solved for both exact and ham homotopy analysis method solutions exact and ham solutions are also compared finally we briefly describe the flow characteristics to include the effects of emerging parameters

a robust colocated implicit algorithm for direct numerical simulation of compressible turbulent flows a non dissipative robust implicit algorithm is proposed for direct numerical and large eddy simulation of compressible turbulent flows the algorithm addresses the problems caused by low mach numbers and under resolved high reynolds numbers it colocates variables in space to allow easy extension to unstructured grids and discretely conserves mass momentum and total energy the navier stokes equations are non dimensionalized using an incompressible scaling for pressure and the energy equation is used to obtain an expression for the velocity divergence a pressure correction approach is used to solve the resulting equations such that the discrete divergence is constrained by the energy equation as a result the discrete equations analytically reduce to the incompressible equations at very low mach number i e the algorithm overcomes the acoustic time scale limit without preconditioning or solution of an implicit system of equations the algorithm discretely conserves kinetic energy in the incompressible inviscid limit and is robust for inviscid compressible turbulence on the convective time scale these properties make it well suited for dns les of compressible turbulent flows results are shown for acoustic propagation the incompressible taylor problem periodic shock tube problem and isotropic turbulence

numerical simulation of isotropic turbulence using a collocated approach and a nonorthogonal grid system we studied the effect of using a nonorthogonal grid coordinate system and a finite volume approach in the simulation of decaying isotropic turbulence calculations were performed in distorted periodic cubic boxes and with a turbulent reynolds number based on the taylor microscale and on a root mean square turbulent velocity of approximately 40 a preliminary study showed that in the nonorthogonal grids some fourier modes of the discretized derivatives can have greater amplitude or the phase inverted relatively to the modes of the exact derivative contrary to what occurs with a cartesian grid system however in the simulations the statistical distributions of velocity pressure and longitudinal and lateral velocity derivatives were always identical regardless of the grid distortion the temporal evolution of the energy was also similar and the differences at the end of the simulations after about two eddy turnover times did not exceed 1 furthermore the grid nonorthogonality affected neither the isotropy of the fields nor the correlation between the vorticity and the principal rates of strain we concluded that the finite volume approach in nonorthogonal grid systems may be used in the numerical simulation of complex turbulent flows with either the direct numerical simulation or large eddy simulation methodologies

higher entropy conservation and numerical stability of compressible turbulence simulations we present a numerical formulation for the treatment of nonlinear instabilities in shock free compressible turbulence simulations the formulation is high order and contains no artificial dissipation numerical stability is enhanced through semi discrete satisfaction of global conservation properties stemming from the second law of thermodynamics and the entropy equation the numerical implementation is achieved using a conservative skew symmetric splitting of the nonlinear terms the robustness of the method is demonstrated by performing unresolved numerical simulations and large eddy simulations of compressible isotropic turbulence at a very high reynolds number results show the scheme is capable of capturing the statistical equilibrium of low mach number compressible turbulent fluctuations at infinite reynolds number comparisons with the entropy splitting technique j comput phys 162 2000 33 j comput phys 178 2002 307 staggered method j comput phys 191 2 2003 392 and skew symmetric like schemes j comput phys 161 2000 114 confirm the superiority of the current approach we also discuss a flaw in the skew symmetric splitting implemented in the literature very good results are obtained based on the proper splitting

an algorithm for piecewise linear approximation of an implicitly defined manifold a simplicial method is used to approximate the solution manifold to a system of nonlinear equations h x theta where h mathbb r n k to mathbb r n the method begins at a point x 0 in the solution set where the derivative dh x 0 is of full rank given any varepsilon 0 a piecewise linear manifold is constructed along which h x infty varepsilon an algorithm is presented to carry out this construction in an efficient fashion

manpak a set of algorithms for computations on implicitly defined manifolds abstract mathematical models often involve differentiable manifolds that are implicitly defined as the solution sets of systems of nonlinear equations the resulting computational tasks differ considerably from those arising for manifolds defined in parametric form here a collection of algorithms is presented for performing a range of essential tasks on general implicitly specified submanifolds of a finite dimensional space this includes algorithms for determining local parametrizations and their derivatives and for evaluating quantities related to the curvature with sensitivity measures the methods have been implemented as a fortran 77 package called manpak

an algorithm for piecewise linear approximation of implicitly defined two dimensional surfaces let h mathbb r n 2 to mathbb r n be a smooth map and let x 0 in h 1 0 be a regular point of h we present an algorithm for obtaining a global piecewise linear approximation to a component m of the surface h 1 0 in particular for a specific type of triangulation t of mathbb r n 2 we construct a component m t subset h t 1 0 where h t is the piecewise linear map that interpolates h on the vertices of t error bounds on h x infty for x in m t are given in terms of the mesh size of t newton type iterative refinement techniques are given for obtaining points on m starting from points on m t sample numerical examples with computer graphical output are given

on the computation of analytical solutions of an unsteady magnetohydrodynamics flow of a third grade fluid with hall effects in this article a combination of lie symmetry and homotopy analysis methods ham are used to obtain solutions for the unsteady magnetohydrodynamics flow of an incompressible electrically conducting third grade fluid bounded by an infinite porous plate in the presence of hall current in particular similarity reductions are performed on the governing equations in its complex scalar and corresponding vector system forms also nontrivial conservation laws using the multiplier approach are constructed for the complex scalar equation furthermore a comparison of the results with numerical results already existing in the literature is done the analytical solutions are presented through graphs by choosing a range of the relevant physical parameters the underlying calculations were obtained via a combination of software packages in mathematica and maple in particular for the lie symmetry generators euler lagrange operators and homotopy operators the latter being towards the construction of the conserved flows

a multilevel algorithm for large eddy simulation of turbulent compressible flows abstract a multilevel method for large eddy simulation of turbulent compressible flows is proposed the method relies on the splitting of the turbulent flowfield into several frequency bands in space and time each band being associated to a specific computational grid in physical space this allows to take into account in a deterministic way the information contained on finer grids a subgrid model adapted to such a decomposition based on a generalization of the germano s identity to multilevel decomposition is also introduced the approach is validated by several multilevel simulations in a subsonic plane channel flow configuration for a low and a high value of the reynolds number while reductions of the cpu times up to 80 are obtained

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 new algorithm for two dimensional numerical continuation abstract consider a smooth mapping f from r n 2 into r n such a mapping can be interpreted as a system of n functions in n 2 unknowns the zero set of the mapping is typically a smooth two dimensional manifold surface embedded in the ambient space of dimension n 2 our paper describes a numerical algorithm for generating a representation of such a surface which can be displayed graphically the defining equations are given in implicit form not only is such a formulation convenient but it allows surfaces with folds in which there is not a functional relationship between the n state space variables and the two distinguished continuation parameters the algorithm is built as a layer on top of an existing one dimensional continuation solver and has been successfully applied to problems with a high dimensional state space using efficient sparse matrix techniques applications in electronic circuit simulation are described

a decreasing sequence of upper bounds for the perron root abstract we obtain a decreasing sequence of upper bounds for the perron root of a nonnegative matrix these upper bounds are new and readily computable for any nonnegative matrix with zero trace the mentioned sequence converges to the perron root we apply these results to the adjacency matrix of a graph

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

revisiting numerical errors in direct and large eddy simulations of turbulence physical and spectral spaces analysis abstract some recent studies on the effects of truncation and aliasing errors on the large eddy simulation les of turbulent flows via the concept of modified wave number are revisited it is shown that all the results obtained for nonlinear partial differential equations projected and advanced in time in spectral space are not straightforwardly applicable to physical space calculations due to the nonequivalence by fourier transform of spectral aliasing errors and numerical errors on a set of grid points in physical space the consequences of spectral static aliasing errors on a set of grid points are analyzed in one dimension of space for quadratic products and their derivatives the dynamical process that results through time stepping is illustrated on the burgers equation a method based on midpoint interpolation is proposed to remove in physical space the static grid point errors involved in divergence forms it is compared to the sharp filtering technique on finer grids suggested by previous authors global performances resulting from combination of static aliasing errors and truncation errors are then discussed for all classical forms of the convective terms in navier stokes equations some analytical results previously obtained on the relative magnitude of subgrid scale terms and numerical errors are confirmed with 3d realistic random fields the physical space dynamical behavior and the stability of typical associations of numerical schemes and forms of nonlinear terms are finally evaluated on the les of self decaying homogeneous isotropic turbulence it is shown that the convective form if conservative properties are not strictly required associated with highly resolving compact finite difference schemes provides the best compromise which is nearly equivalent to dealiased pseudo spectral calculations

enhancement of an industrial finite volume code for large eddy type simulation of incompressible high reynolds number flow using near wall modelling abstract we present a validation strategy for enhancement of an unstructured industrial finite volume solver designed for steady rans problems for large eddy type simulation with near wall modelling of incompressible high reynolds number flow different parts of the projection based discretisation are investigated to ensure les capability of the numerical method turbulence model parameters are calibrated by using a minimisation of least squares functionals for first and second order statistics of the basic benchmark problems decaying homogeneous turbulence and turbulent channel flow then the method is applied to the flow over a backward facing step at reh 37 500 of special interest is the role of the spatial and temporal discretisation error for low order schemes for wall bounded flows present results confirm existing best practice guidelines for mesh design for free shear layers a sensor to quantify the resolution quality of the les based on the resolved turbulent kinetic energy is presented and applied to the flow over a backward facing step at reh 37 500

b spline method and zonal grids for simulations of complex turbulent flows a numerical technique for computations of turbulent flows is described the technique is based on b splines and allows grid embedding in physically significant flow regions numerical tests which include solutions of nonlinear advection diffusion equations and computations of flow over a circular cylinder at reynolds numbers up to 300 indicate that the method is accurate and efficient in computations of flow over a cylinder the lift drag and base suction coefficients agree well with existing experimental data and previous numerical simulations

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

large eddy simulation of a spatially evolving supersonic turbulent boundary layer flow several issues involving the large eddy simulation of wall bounded compressible turbulent flows are investigated a spatially evolving supersonic boundary layer is simulated using a high order accurate finite difference scheme and the dynamic subgrid scale model a parametric study suggests that the finite difference scheme has a detrimental effect on the resolution of the smaller scales due to excessive numerical dissipation from the spatial differencing also because the dynamic model uses the smaller resolved scale eddies to determine the model coefficients the predicted coefficients do not have the appropriate values the use of higher order schemes is found to better capture the smaller resolved scales and to improve substantially the quality of the results the effect of descretization errors on large eddy simulation needs to be addressed further before proceeding with large eddy simulation of flows of engineering interest

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

stabilized non dissipative approximations of euler equations in generalized curvilinear coordinates we discuss stabilization strategies for finite difference approximations of the compressible euler equations in generalized curvilinear coordinates that do not rely on explicit upwinding or filtering of the physical variables our approach rather relies on a skew symmetric like splitting of the convective derivatives that guarantees preservation of kinetic energy in the semi discrete low mach number limit a locally conservative formulation allows efficient implementation and easy incorporation into existing compressible flow solvers the validity of the approach is tested for benchmark flow cases including the propagation of a cylindrical vortex and the head on collision of two vortex dipoles the tests support high accuracy and superior stability over conventional central discretization of the convective derivatives the potential use for dns les of turbulent compressible flows in complex geometries is discussed

comparison of conservative and rotational forms in large eddy simulation of turbulent channel flow abstract fully developed turbulent channel flow is studied numerically using large eddy simulation les with a fourier finite difference method a prominent feature of this paper lies in the use of a conservative form of the arakawa type for the convective terms in the navier stokes equations the results are compared with earlier ones of moin and kim 1 based on the rotational form of the convective terms noticeable differences are found in quantities such as turbulence intensities two point correlations etc the difference is most prominent in the grid scale portion of the turbulent shear stress the present results agree well with the recent direct simulation of a mildly curved channel flow by moser and moin 2 using the fourier chebyshev polynomial expansions an estimate is made of the error inherent in the rotational form combined with the second order central finite difference method the relationship between the energy production mechanism and helicity is pointed out

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized

a further study of numerical errors in large eddy simulations numerical errors in large eddy simulations les arise from aliasing and discretization errors and errors in the subfilter scale sfs turbulence model using a direct numerical simulation dns dataset of stably stratified shear flow to perform a priori tests we compare the numerical error from several finite difference schemes to the magnitude of the sfs force this is an extension of ghosal s analysis j comput phys 125 1996 187 to realistic flow fields by evaluating different grid resolutions as well as different filter grid ratios we provide guidelines for les for a second order finite difference scheme a filter grid ratio of at least four is desired for a sixth order pade scheme a filter grid ratio of two is sufficient

the computation of simplicial approximations of implicitly defined p dimensional manifolds abstract a method is presented for the computation of a simplicial approximation covering a subset m 0 of a p dimensional manifold m in r n defined implicitly as the solution set of a nonlinear system f x 0 of n p equations in n unknowns n p 2 the subset m 0 is either the intersection of m with some polyhedral domain in r n and is assumed to be bounded and nonempty or it is an entire manifold component which has no boundary such as a sphere the method represents a generalization of a simplicial approximation process for the case p 2 developed earlier by the author and w rheinboldt

numerical convergence of the lyapunov spectrum computed using low mach number solvers abstract in the dynamical systems approach to describing turbulent or otherwise chaotic flows an important quantity is the lyapunov exponents and vectors that characterize the strange attractor of the flow in particular knowledge of the lyapunov exponents and vectors will help identify perturbations that the system is most sensitive to and quantify the dimension of the attractor however reliably computing these quantities requires robust numerical algorithms while several perturbation based techniques are available in literature their application to commonly used turbulent flow solvers as well the numerical convergence properties have not been studied in detail the goal of this work is to examine the convergence properties of the lyapunov exponents when computed using a low mach number solver for a series of progressively complex flow problems in particular a manufactured solutions approach is devised using the orr sommerfeld os perturbation theory to extract lyapunov exponents and vectors from os eigen solutions overall the spatial convergence rates of lyapunov exponents follow the truncation order for the discretization scheme however temporal convergence rates were found to be only a weak function of timestep used additionally for some configurations the convergence properties are found to depend on the lyapunov exponent itself these results indicate that convergence properties do not follow universal rates and require careful analysis for specific configurations considered