pseudo time stepping methods for space time discontinuous galerkin discretizations of the compressible navier stokes equations the space time discontinuous galerkin discretization of the compressible navier stokes equations results in a non linear system of algebraic equations which we solve with pseudo time stepping methods we show that explicit runge kutta methods developed for the euler equations suffer from a severe stability constraint linked to the viscous part of the equations and propose an alternative to relieve this constraint while preserving locality to evaluate its effectiveness we compare with an implicit explicit runge kutta method which does not suffer from the viscous stability constraint we analyze the stability of the methods and illustrate their performance by computing the flow around a 2d airfoil and a 3d delta wing at low and moderate reynolds numbers

a multi scale formulation for compressible turbulent flows suitable for general variational discretization techniques based on the recently introduced variational multi scale vms approach to large eddy simulation les as introduced in t j r hughes l mazzei k e jansen large eddy simulation and the variational multiscale method comput visual sci 3 2001 47 59 s s collis monitoring unresolved scales in multiscale turbulence modeling phys fluids 13 6 2001 1800 1806 we present a vms formulation which can be used in the simulation of compressible flows special attention is given to obtain a vms formulation which is suitable for complex flow domains and general variational discretization techniques a generalization of the favre averaging procedure is introduced such that the formulation resembles the favre filtered navier stokes equations traditionally used in les of compressible flow and no explicit subgrid terms arise in the continuity equation also we show that with the use of discretization methods other than fourier spectral methods the vms projection no longer commutes with differentiation this results in additional subgrid scale terms which resemble the commutator error as encountered in the traditional filtering approach to les

turbulence control simulation using the variational multiscale method the capabilities of the variational multiscale vms method are explored in the context of turbulence control by applying vms to the simulation of a simple opposition control strategy for turbulent channel flow with the results compared to prior direct numerical simulations and large eddy simulations based on the dynamic subgrid scale model in all cases the vms method is found to be more efficient and more accurate than the dynamic model and the simplicity accuracy and generality of vms makes it particularly attractive for turbulence control investigations

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

the use of explicit filters in large eddy simulation abstract explicit filtering is considered as a means of controlling the numerical errors that result when finite difference methods are used in large eddy simulation les the notion that the finite difference expressions themselves act as an effective filter is shown to be false for three dimensional simulations performed on nonuniform meshes for consistency the nonlinear terms in the navier stokes equations should be filtered explicitly at each time step in order to insure that the spectral content of the solution remains fixed at the desired filter level the explicit filtering operation allows a separation between the filter size and the mesh spacing and can be used to control the impact of the numerical errors numerical tests of the explicit filtering approach in turbulent channel flow are used to investigate the effectiveness of the explicit filtering approach and to assess its associated cost explicit filtering is shown to improve the computed results but this improvement comes at a rather high computational cost the explicitly filtered approach is also compared with straightforward mesh refinement as an alternative means of improving the computed results mesh refinement is also seen to increase the accuracy of the simulation but some traces of numerical error appear to persist in the solution

a variational multiscale stabilized finite element method for the solution of the euler equations of nonhydrostatic stratified flows we present a compressible version of the variational multiscale stabilization vms method applied to the finite element fe solution of the euler equations for nonhydrostatic stratified flows this paper is meant to verify how the algorithm performs when solving problems in the framework of nonhydrostatic atmospheric dynamics this effort is justified by the previously observed good performance of vms and by the advantages that a compact galerkin formulation offers on massively parallel architectures a paradigm for both computational fluid dynamics cfd and numerical weather prediction nwp practitioners we also propose a simple technique to construct a well balanced approximation of the dominant hydrostatics that if not properly discretized may cause unacceptable vertical oscillations this is a relevant problem in nwp especially in the proximity of steep topography to evaluate the performance of the method for stratified environments six standard 2d and two 3d test cases are selected of these two admit a semi analytic solution while the remaining six are non steady and non linear thermal problems with dominant buoyancy effects that challenge the algorithm in terms of stability

on boundary hybrid finite element methods for the laplace equation abstract about two decades ago i babuska j t oden and j k lee introduced finite element methods that calculate the normal derivative of the solution along the mesh interfaces and recover the solution via local neumann problems these methods for the treatment of the homogeneous laplace equation were called boundary hybrid methods the approach was revisited in 12 for general symmetric and positive definite elliptic equations with homogeneous boundary conditions the new approximation is nonconforming and lends itself well for an a posteriori error estimator for conforming finite element approximations numerical tests presented in 12 corroborated that the error estimates are accurate and cheap for conforming approximations this paper provides the iterative solution methods and galerkin discretization methods on which the numerical approximations in 12 were based

mathematical and physical constraints on large eddy simulation of turbulence recent progress in the theoretical foundations of large eddy simulation is reviewed most of the work reported is motivated by conceptual difficulties encountered in applying the large eddy simulation method to inhomogeneous complex geometry flows among the topics covered are the problem of the lack of commutation between filtering and derivative operators for inhomogeneous flows the issues of enforcing symmetry and realizability conditions in subgrid modeling and the problem of unacceptably high numerical errors in large eddy simulation implementations with finite difference methods

space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows i general formulation a new space time discontinuous galerkin finite element method for the solution of the euler equations of gas dynamics in time dependent flow domains is presented the discontinuous galerkin discretization results in an efficient elementwise conservative upwind finite element method which is particularly well suited for local mesh refinement the upwind scheme uses a formulation of the hllc flux applicable to moving meshes and several formulations for the stabilization operator to ensure that monotone solutions around discontinuities are investigated the non linear equations of the space time discretization are solved using a multigrid accelerated pseudo time integration technique with an optimized runge kutta method the linear stability of the pseudo time integration method is investigated for the linear advection equation the numerical scheme is demonstrated with simulations of the flow field in a shock tube a channel with a bump and an oscillating naca 0012 airfoil these simulations show that using the data at the superconvergence points the accuracy of the numerical discretization is o h5 2 in space for smooth subsonic flows both on structured and on locally refined meshes and that the space time adaptation can significantly improve the accuracy and efficiency of the numerical method

observing non linear time variable systems through a canonical form observer abstract bestle and zeitz have introduced a non linear time variable observer canonical form which permits through a non linear state transformation the use of the eigenvalue assignment method to design observers for non linear time variable dynamic systems in this paper a necessary and sufficient condition under which the transformation exists is given it is also proved that the transformation could be determined by integrating single variable functions instead of solving a set of partial differential equations as shown by bestle and zeitz examples are included to show how to do the transformation

a variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes application to vortex shedding the variational multiscale formulation of large eddy simulations developed by hughes and his co workers for incompressible turbulent flows is first extended to the case of compressible turbulent flows next a finite volume element discretization on tetrahedral meshes of this method is proposed this discretization features an economical procedure based on agglomeration for separating a priori the scales a corresponding projector for eliminating the small scales from the system of equations and an effective control of the numerical dissipation induced by upwinding the resulting les method is validated with the three dimensional numerical simulation of a low speed flow past a square cylinder at m 0 1 and re 22 000 and various comparisons with experimental data

the basic equations for the large eddy simulation of turbulent flows in complex geometry abstract the equations for large eddy simulation les of turbulent flows are derived by applying a filtering operation to the navier stokes equations les of inhomogeneous turbulent flows requires the use of filters with variable filter width the use of such filters invalidates the standard derivation of the basic equations for the filtered fields since the filtering operation in general does not commute with the operation of differentiation in this paper an alternate definition of the filtering operation based on the mapping function of the nonuniform grid is introduced it is shown that with this modified definition the filtering and differentiation operations commute up to an error which is second order in the filter width it is also shown that the commutation error can be expressed in terms of the filtered field and its derivatives as an asymptotic series in the square of the filter width these results are then applied to the navier stokes equations to derive the basic equations satisfied by the filtered fields

a note on non linear observers a general non linear exponential observer is presented for non linearly perturbed nonlinear systems this is done by using the non linear variation of constants formula

implicit large eddy simulation of non wall bounded turbulent flows based on the multiscale properties of a high order finite volume method in this paper it is presented the application of a higher order finite volume method based on moving least squares approximations fv mls to the resolution of non wall bounded compressible turbulent flows our approach is based on the monotonically implicit large eddy simulation miles the main idea of miles methodology is the absence of any explicit subgrid scale sgs model in the numerical algorithm to solve turbulent flows in the case of the fv mls method we take advantage of the multiresolution properties of moving least squares approximations and we show that they can be used as an implicit sgs model the numerical results are encouraging the third order fv mls method is able to reproduce the inertial subrange and it obtains better results than other usual numerical schemes in les computations such as the muscl scheme we note that in the present state of this research the numerical method is not yet suited for wall bounded flows this paper is the first step in the application of the fv mls method to general turbulent flows

computational error analysis of a discontinuous galerkin discretization applied to large eddy simulation of homogeneous turbulence a computational error assessment of large eddy simulation les in combination with a discontinuous galerkin finite element method is presented for homogeneous isotropic decaying turbulence the error landscape database approach is used to quantify the total simulation error that arises from the use of the smagorinsky eddy viscosity model in combination with the galerkin discretization we adopt a modified hllc flux allowing an explicit control over the dissipative component of the numerical flux the optimal dependence of the smagorinsky parameter on the spatial resolution is determined for second and third order accurate galerkin methods in particular the role of the numerical dissipation relative to the contribution from the smagorinsky dissipation is investigated we observed an exchange of dissipation principle in the sense that an increased numerical dissipation implied a reduction in the optimal smagorinsky parameter the predictions based on galerkin discretization with fully stabilized hllc flux were found to be less accurate than when a central discretization with mainly smagorinsky dissipation was used this was observed for both the second and third order galerkin discretization suggesting to emphasize central discretization of the convective nonlinearity and stabilization that mimics eddy viscosity as sub filter dissipation

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

a dynamic variational multiscale method for large eddy simulations on unstructured meshes abstract a dynamic version of the variational multiscale vms method for large eddy simulation les on unstructured meshes of turbulent compressible flows is presented its key features include two variational analogues of germano s algebraic identity and a computationally efficient agglomeration based numerical procedure agglomeration is used both for separating a priori the scales and computing dynamically a smagorinsky parameter and the turbulent prandtl number on unstructured finite volume or finite element meshes numerical predictions of low speed 20 angle of attack turbulent flows past a 6 1 prolate spheroid and a forward swept scaled wing are presented they are contrasted with counterpart results obtained using similar implementations on unstructured meshes of the vms les traditional les and traditional dynamic les methods they are also compared to experimental data when available

space time discontinuous galerkin method for the compressible navier stokes equations a space time discontinuous galerkin finite element method for the compressible navier stokes equations is presented we explain the space time setting derive the weak formulation and discuss our choices for the numerical fluxes the resulting numerical method allows local grid adaptation as well as moving and deforming boundaries which we illustrate by computing the flow around a 3d delta wing on an adapted mesh and by simulating the dynamic stall phenomenon of a 2d airfoil in rapid pitch up maneuver

local preconditioning and variational multiscale stabilization for euler compressible steady flow abstract this paper introduces a preconditioned variational multiscale stabilization p vms method for compressible flows in this introductory paper we focus on inviscid flow and steady state problems the euler equations are solved on fully unstructured grids and discretized using the finite element method the p vms method can be decomposed into three parts first a local preconditioner is applied to the continuous equations to reduce the stiffness while covering a wide range of mach numbers then the resulting preconditioned system is discretized in space using finite elements and stabilized with a variational multiscale stabilization method adapted for the preconditioned equations in this paper the solution is advanced in time using a fully explicit time discretization although p vms is general and can be applied to fully implicit solvers the proposed method is assessed by comparing convergence and accuracy of the solutions between the non preconditioned and preconditioned cases in particular for van leer lee roe s 1991 and choi merkle s 1993 preconditioners in some selected examples covering a large range of mach numbers

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