isogeometric variational multiscale modeling of wall bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes abstract in this work we combine i nurbs based isogeometric analysis ii residual driven turbulence modeling and iii weak imposition of no slip and no penetration dirichlet boundary conditions on unstretched meshes to compute wall bounded turbulent flows while the first two ingredients were shown to be successful for turbulence computations at medium to high reynolds number i akkerman y bazilevs v m calo t j r hughes s hulshoff the role of continuity in residual based variational multiscale modeling of turbulence comput mech 41 2008 371 378 y bazilevs v m calo j a cottrell t j r hughes a reali g scovazzi variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows comput methods appl mech engrg 197 2007 173 201 it is the weak imposition of no slip boundary conditions on coarse uniform meshes that maintains the good performance of the proposed methodology at higher reynolds number y bazilevs t j r hughes weak imposition of dirichlet boundary conditions in fluid mechanics comput fluids 36 2007 12 26 y bazilevs c michler v m calo t j r hughes weak dirichlet boundary conditions for wall bounded turbulent flows comput methods appl mech engrg 196 2007 4853 4862 these three ingredients form a basis of a possible practical strategy for computing engineering flows somewhere between rans and les in complexity we demonstrate this by solving two challenging incompressible turbulent benchmark problems channel flow at friction velocity reynolds number 2003 and flow in a planar asymmetric diffuser we observe good agreement between our calculations of mean flow quantities and both reference computations and experimental data this lends some credence to the proposed approach which we believe may become a viable engineering tool

an algebraic variational multiscale multigrid method for large eddy simulation of turbulent flow an algebraic variational multiscale multigrid method for large eddy simulation of turbulent flow

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

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

enforcement of constraints and maximum principles in the variational multiscale method abstract we present a new theoretical framework for the enforcement of constraints in variational multiscale vms analysis the theory is first presented in an abstract operator format and subsequently specialized for the steady advection diffusion equation the approach borrows heavily from results in constrained and convex optimization an exact expression for the fine scales is derived in terms of variational derivatives of the constraints lagrange multipliers and a fine scale green s function the methodology described enables the development of numerical methods which satisfy predefined attributes a practical and effective procedure for solving the steady advection diffusion equation is presented based on a vms inspired stabilized method weakly enforced dirichlet boundary conditions and enforcement of a maximum principle and conservation constraint

chord arc surfaces with small constant ii good parameterizations abstract in a companion paper we introduced a notion for hypersurfaces in r d 1 that is analogous to the chord arc condition with small constant for planar curves in this paper we address the problem of finding good parameterizations for these surfaces in particular we show that these surfaces must be homeomorphic to r d and we build parameterizations with l p bounds on the gradient and the gradient of the inverse with p as the chord arc constant goes to 0 when d 2 we use the uniformization theorem to find a quasisymmetric parameterization we do not know how to build bilipschitz parameterizations when d 2 or quasisymmetric parameterizations when d 3 the author conjectures that they do not exist in general however we can build bilipschitz reflections in all dimensions and these reflections will satisfy certain extra estimates in terms of carleson measures

an algebraic variational multiscale multigrid method for large eddy simulation of turbulent variable density flow at low mach number an algebraic variational multiscale multigrid method is proposed for large eddy simulation of turbulent variable density flow at low mach number scale separating operators generated by level transfer operators from plain aggregation algebraic multigrid methods enable the application of modeling terms to selected scale groups here the smaller of the resolved scales in a purely algebraic way thus for scale separation no additional discretization besides the basic one is required in contrast to earlier approaches based on geometric multigrid methods the proposed method is thoroughly validated via three numerical test cases of increasing complexity a rayleigh taylor instability turbulent channel flow with a heated and a cooled wall and turbulent flow past a backward facing step with heating results obtained with the algebraic variational multiscale multigrid method are compared to results obtained with residual based variational multiscale methods as well as reference results from direct numerical simulation experiments and les published elsewhere particularly mean and various second order velocity and temperature results obtained for turbulent channel flow with a heated and a cooled wall indicate the higher prediction quality achievable when adding a small scale subgrid viscosity term within the algebraic multigrid framework instead of residual based terms accounting for the subgrid scale part of the non linear convective term

behavior near the boundary of positive solutions of second order parabolic equations ii a boundary backward harnack inequality is proved for positive solutions of second order parabolic equations in non divergence form in a bounded cylinder q q x 0 t which vanish on o q oq x 0 t where q is a bounded lipschitz domain in r this inequality is applied to the proof of the holder continuity of the quotient of two positive solutions vanishirlg on a portion of o q

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

scale separating operators for variational multiscale large eddy simulation of turbulent flows a general class of scale separating operators based on combined multigrid operators is proposed and analyzed in this work the operators of this class are designed for variational multiscale large eddy simulation using a finite volume or finite element method two representatives are compared to discrete smooth filters which are widely used in the traditional large eddy simulation literature the comparison shows that they are not only theoretically different but also yield considerable differences in the respective numerical results dynamic as well as constant coefficient based subgrid scale modeling is used within the multiscale environment all of the scale separating operators are implemented in a second order accurate energy conserving finite volume method and tested for the case of a turbulent channel flow one operator shows particularly remarkable results in the framework of the variational multiscale large eddy simulation that is profiles are obtained for velocity and kinetic energy which are considerably closer to the respective profiles from a direct numerical simulation than are the profiles resulting from the application of the other operators considered in the present study furthermore this particular operator proves to be very efficient with regard to the important aspect of computational cost that is a reduction in computing time ranging from about 25 up to about 150 compared to the other operators the introduction of a substantial amount of subgrid viscosity to the small scales particularly in the buffer layer of the channel appears to be crucial for the good results achieved with this method

two types of discrete sobolev inequalities on a weighted toeplitz graph abstract in this paper two types of discrete sobolev inequalities that correspond to the generalized graph laplacian a on a weighted toeplitz graph are obtained the sharp constants c 0 a and c 0 are calculated using the green matrix g a a a i 1 0 a and pseudo green matrix g a penrose moore generalized inverse matrix of a the sharp constants are expressed as reciprocals of the harmonic mean corresponding to eigenvalues of each matrix a a i and a except an eigenvalue 0

correct energy evolution of stabilized formulations the relation between vms supg and gls via dynamic orthogonal small scales and isogeometric analysis i the convective diffusive context this paper presents the construction of novel stabilized finite element methods in the convective diffusive context that exhibit correct energy behavior classical stabilized formulations can create unwanted artificial energy our contribution corrects this undesired property by employing the concepts of dynamic as well as orthogonal small scales within the variational multiscale framework vms the desire for correct energy indicates that the large and small scales should be h 0 1 orthogonal using this orthogonality the vms method can be converted into the streamline upwind petrov galerkin supg or the galerkin least squares gls method incorporating both large and small scales in the energy definition asks for dynamic behavior of the small scales therefore the large and small scales are treated as separate equations two consistent variational formulations which depict correct energy behavior are proposed i the galerkin least squares method with dynamic small scales glsd and ii the dynamic orthogonal formulation do the methods are presented in combination with an energy decaying generalized time integrator numerical verification shows that dissipation due to the small scales in classical stabilized methods can become negative on both a local and a global scale the results show that without loss of accuracy the correct energy behavior can be recovered by the proposed methods the computations employ nurbs based isogeometric analysis for the spatial discretization

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

spectral analysis of the dissipation of the residual based variational multiscale method abstract we analyze the application of the residual based variational multiscale vms method to the solution of a generic partial differential equation we prove that the model terms introduced by this method are dissipative under certain restrictions that are likely to be satisfied by spectral approximations of conservation laws in particular we demonstrate that the fourier spectral approximations of burgers equation and the incompressible navier stokes equations satisfy these conditions hence we show that the residual based vms model for these equations is dissipative even though the form of the model term does not resemble an eddy viscosity we analyze the scale dependence of this dissipation using fully resolved numerical solutions and conclude that the vms model accurately captures the scale dependence of the cross stress terms u u and under predicts the contribution from the reynolds stress terms u u these observations have implications on the use of the residual based vms method in spectral approximations of nonlinear conservation laws

a discontinuous galerkin method with lagrange multipliers for spatially dependent advection diffusion problems abstract a higher accuracy discontinuous galerkin method with lagrange multipliers dglm is presented for the solution of the advection diffusion equation with a spatially varying advection field in the high peclet number regime where the classical polynomial finite element method fem produces spurious oscillations in the solution at practical mesh resolutions the proposed dglm method is based on discontinuous polynomial shape functions that are attached to an element rather than its nodes it overcomes the aforementioned spurious oscillation issue by enriching these functions with approximate free space solutions of homogeneous equations derived from an asymptotic analysis of the governing partial differential equation inspired by prandtl s boundary layer theory these enrichment functions are capable of resolving exponential parabolic and corner boundary layers at relatively coarse mesh resolutions the proposed method enforces a weak continuity of the solution approximation across inter element boundaries using polynomial lagrange multipliers which makes it a hybrid method however unlike other hybrid methods it operates directly on the second order form of the advection diffusion equation and does not require any stabilization its intrinsic performance and its superiority over the higher order polynomial fem are demonstrated for several test problems at peclet numbers ranging from one thousand to one billion

green s matrices abstract our goal is to identify and understand matrices a that share essential properties of the unitary hessenberg matrices m that are fundamental for szego s orthogonal polynomials those properties include i recurrence relations connect characteristic polynomials rk x of principal minors of a ii a is determined by generators parameters generalizing reflection coefficients of unitary hessenberg theory iii polynomials rk x correspond not only to a but also to a certain cmv like five diagonal matrix iv the five diagonal matrix factors into a product bc of block diagonal matrices with 2 2 blocks v submatrices above and below the main diagonal of a have rank 1 vi a is a multiplication operator in the appropriate basis of laurent polynomials vii eigenvectors of a can be expressed in terms of those polynomials conditions v connects our analysis to the study of quasi separable matrices but the factorization requirement iv narrows it to the subclass of green s matrices that share properties i vii the key tool is twist transformations that provide 2n matrices all sharing characteristic polynomials of principal minors with a one such twist transformation connects unitary hessenberg to cmv another twist transformation explains findings of fiedler who noticed that companion matrices give examples outside the unitary hessenberg framework we mention briefly the further example of a daubechies wavelet matrix infinite matrices are included

chord arc surfaces with small constant i abstract we introduce a notion for hypersurfaces in r d 1 that is analogous to the chord arc condition with small constant for curves in the plane we give various equivalent operator theoretic function theoretic and geometrical characterizations of these surfaces we not know any nice potential theoretic characterizations in a companion paper we address the issue of finding good parameterizations for these surfaces

harmonic measure on locally flat domains we will review work with tatiana toro yielding a characterizati on of those domains for which the harmonic measure has a density whose logarithm has vanishing mean oscillation

a consistent dynamic localization model for large eddy simulation of turbulent flows based on a variational formulation in this study a new approach for the dynamic localization model which was originally proposed in ghosal et al s ghosal t s lund p moin k akselvoll a dynamic localization model for large eddy simulation of turbulent flows j fluid mech 286 1995 229 255 is described this approach is integrated in a consistent manner into large eddy simulation based on a variational formulation as a result the variationally formulated condition for the model parameter is considered as an additional equation in a resulting system of two variational equations this variational system may then be implemented using either a finite element or a finite volume method the new version of the dynamic localization model proposed in this work has three advantages compared to the original dynamic localization model in ghosal et al it relies on a simpler formulation overall it obviates any iterative solution procedure and it requires the solution of a number of small independent local equations instead of one large global equation these three advantages make its solution theoretically easier and computationally more efficient the new consistent dynamic localization model is tested for two different numerical flow examples turbulent flow in a channel and turbulent flow in a planar asymmetric diffuser

a linearized method for the frequency analysis of three dimensional fluid structure interaction problems in all flow regimes abstract we present a computational fluid dynamics cfd based linearized method for the frequency analysis of three dimensional fluid structure interaction problems this method is valid in the subsonic transonic and supersonic flow regimes and is insensitive to the frequency or damping level of the sought after coupled eigenmodes it is based on the solution by an orthogonal iteration procedure of a complex eigenvalue problem derived from the linearization of a three field fluid structure moving mesh formulation the key computational features of the proposed method include the reuse of existing unsteady flow solvers a second order approximation of the flux jacobian matrix and a parallel domain decomposition based iterative solver for the solution of large scale systems of discretized fluid structure equations while the frequency analysis method proposed here is primarily targeted at the extraction of the eigenpairs of a wet structure we validate it with the flutter analysis of the agard wing 445 6 for which experimental data is available

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

caloric measure in parabolic flat domains in this paper we define parabolic chord arc domains and show that in a parabolic chord arc domain with vanishing constant the logarithm of the density of caloric measure with respect to a certain projective lebesgue measure is of vanishing mean oscillation we also obtain a partial converse to this result our work generalizes to the heat equation recent work of kenig and toro for the laplacian

a scalable feti dp algorithm with non penetration mortar conditions on contact interface by combining feti algorithms of dual primal type with recent results for bound constrained quadratic programming problems we develop an optimal algorithm for the numerical solution of coercive variational inequalities the model problem is discretized using non penetration conditions of mortar type across the potential contact interface and a feti dp algorithm is formulated the resulting quadratic programming problem with bound constraints is solved by a scalable algorithm with a known rate of convergence given in terms of the spectral condition number of the quadratic problem numerical experiments for non matching meshes across the contact interface confirm the theoretical scalability of the algorithm

gram matrices of reproducing kernel hilbert spaces over graphs in this paper we introduce the notion of reproducing kernel hilbert spaces for graphs and the gram matrices associated with them our aim is to investigate the gram matrices of reproducing kernel hilbert spaces we provide several bounds on the entries of the gram matrices of reproducing kernel hilbert spaces and characterize the graphs which attain our bounds

a stabilized mixed discontinuous galerkin method for darcy flow abstract a new mixed stabilized discontinuous galerkin formulation for darcy flow is presented the formulation combines several attributes not simultaneously satisfied by other methods it is convergent for any combination of velocity and pressure interpolation higher than first order it exactly satisfies a mass balance on each element and it passes two and three dimensional constant flow patch tests for distorted element geometries the key ingredient in the formulation is a volumetric residual based stabilization term that does not involve any mesh dependent parameters

a fully coupled rans spalart allmaras supg formulation for turbulent compressible flows on stretched unstructured grids abstract when high reynolds turbulent flows are combined with complex and large size geometries computers are no longer enough powerful to deal with direct numerical simulation dns and with the resolution of all the scales of turbulence motion therefore the rans approaches solve averaged equations and use a model to simulate these scales this model contains dissipation processes that should not be polluted by the numerical diffusion needed to stabilized approximations for convection dominated flows in this paper we proposed a strongly coupled numerical formulation for the spalart allmaras model in the framework of stabilized finite element methods computations are performed for compressible newtonian fluids 2d and 3d on unstructured grids of high aspect ratio results are compared with experimental data and also with solutions obtained by different numerical strategies

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 modal based multiscale method for large eddy simulation we introduce a modal spectral element method which employs the variational multiscale approach for large eddy simulation the method is sufficiently general for application to complex flow geometries but requires relatively few degrees of freedom for a given mesh and polynomial order we investigate the performance of the method for fully developed turbulent channel flow it is shown that large increases in accuracy can be obtained when the basic dynamics of near wall coherent structures can be represented using the portion of the modal basis which is free of the subgrid scale model this implies that in spite of its lack of orthogonality the modal basis provides sufficient scale separation to exploit the advantages of the variational multiscale approach

residual based vms subgrid modeling for vortex flows this paper presents a residual based subgrid modeling approach for large eddy simulations les based on the variational multiscale method as a cure for the problem of preservation of vortices in numerical flow simulation this approach combines a splitting of the non linear term in the navier stokes equations into strain and vorticity with a residual based modeling of the subgrid problems the benefit is that certain driving phenomena normally not present in subgrid modeling e g vortex stretching can be seen in the equations here we focus on two of the subgrid terms arising from the subgrid scale problem the effect of the two terms are illustrated in an les of a three dimensional flow around a wing where the main feature is the formation and preservation of a tip vortex an important phenomenon in many aerodynamic and hydrodynamical applications we see that the addition of the new subgrid terms correctly counteracts the dissipative effect arising from numerics and turbulence modeling on the vortex and thus strongly improves prediction of the tip vortex c 2009 elsevier b v all rights reserved

residual based variational multiscale turbulence models for unstructured tetrahedral meshes abstract this paper presents three level residual based turbulence models for the incompressible navier stokes equations employing the variational multiscale vms framework the velocity and pressure fields are decomposed into two overlapping hierarchical scales thereby leading to a system of coupled mixed field problems the mixed problem at the fine scales is stabilized via a subsequent vms application that results in a further decomposition of the fine scale velocity field into level i and level ii scales the level ii scales are modeled using higher order bubble functions that are then variationally embedded in the level i formulation to stabilize it the level i problem is modeled via a second set of bubble functions that are linearly independent of the bubbles employed at level ii finally the resulting level i fine scales are variationally embedded in the coarse scale formulation this yields a residual based turbulence model for the larger or coarser scales a significant feature of the proposed method is that it results in a concurrent top down and bottom up two way nesting of the scales in addition the resulting turbulence model does not possess any embedded tunable parameters another attribute of the formulation is that the fine scales at every level are driven by the residuals of the euler lagrange equations of the coarser scales at the preceding levels thereby resulting in a method that is variationally consistent various algorithmic generalizations of the method are presented that lead to computationally economic residual based turbulence models the proposed telescopic depth in scales approach helps make these models accurate for low order tetrahedral and hexahedral elements a feature that is facilitated by the higher order bubble functions over element interiors and it results in an enhanced representation of the fine scale terms modeling the fine viscous effects from a computational perspective this method results in easy to implement equal order pressure velocity elements and possesses the desirable p refinement feature numerical performance of the method is assessed on turbulent channel flow problems at re 395 and re 590 also presented are the results for turbulent sd 7003 airfoil at re 60 000 and comparison is made with the published experimental data and numerical results

a high order discontinuous galerkin method with lagrange multipliers for advection diffusion problems abstract a high order discontinuous galerkin method with lagrange multipliers dglm is presented for the solution of advection diffusion problems on unstructured adaptive meshes unlike other hybrid discretization methods for transport problems it operates directly on the second order form the advection diffusion equation like the discontinuous enrichment method dem it chooses the basis functions among the free space solutions of the homogeneous form of the governing partial differential equation and relies on lagrange multipliers for enforcing a weak continuity of the approximated solution across the element interface boundaries however unlike dem the proposed hybrid discontinuous galerkin method approximates the lagrange multipliers in a space of polynomials instead of a space of traces on the element boundaries of the normal derivatives of a subset of the basis functions for a homogeneous problem the design of arbitrarily high order elements based on this dglm method is supported by a detailed mathematical analysis for a non homogeneous one the approximated solution is locally decomposed into its homogeneous and particular parts the homogeneous part is captured by the dglm elements designed for a homogenous problem the particular part is obtained analytically after the source term is projected onto an appropriate polynomial space this decoupling between the two parts of the solution is another differentiator between dglm and dem with attractive computational advantages an a posteriori error estimator for the proposed method is also derived to enable adaptive mesh refinement all theoretical results are illustrated by numerical simulations that furthermore highlight the potential of the proposed high order hybrid dg method for transport problems with steep gradients in the high peclet number regime

computation of unsteady viscous flows around moving bodies using the k e turbulence model on unstructured dynamic grids abstract we consider the numerical solution on unstructured dynamic meshes of the averaged navier stokes equations equipped with the k e turbulence model and a wall function we discuss discretization issues pertaining to conservation laws moving grids and numerical dissipation we also present a robust spring analogy method for constructing dynamic meshes we validate our implementation of this two equation turbulence model and justify its usage for a class of vortex shedding problems by correlating our computational results with experimental data obtained for a flow past a square cylinder we also apply our solution methodology to the two dimensional aerodynamic stability analysis of the tacoma narrows bridge and report numerical results that are in good agreement with observed data

a multiscale finite element method for the incompressible navier stokes equations this paper presents a new multiscale finite element method for the incompressible navier stokes equations the proposed method arises from a decomposition of the velocity field into coarse resolved scales and fine unresolved scales modeling of the unresolved scales corrects the lack of stability of the standard galerkin formulation and yields a method that possesses superior properties like that of the streamline upwind petrov galerkin supg method and the galerkin least squares gls method the multiscale method allows arbitrary combinations of interpolation functions for the velocity and the pressure fields specifically the equal order interpolations that are easy to implement but violate the celebrated babuska brezzi condition a significant feature of the present method is that the structure of the stabilization tensor s appears naturally via the solution of the fine scale problem a family of 2 d elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed convergence studies for the method on uniform skewed as well as composite meshes are presented numerical simulations of the nonlinear steady and transient flow problems are shown that exhibit the good stability and accuracy properties of the method 2005 elsevier b v all rights reserved

an entropy variable based vms gls method for the simulation of compressible flows on unstructured grids abstract the variational multiscale approach for large eddy simulation is investigated within a finite element framework a filtering analog of this method providing a model which shares basic structures with hyperviscosity models is used and evaluated on a freely decaying isotropic turbulence in the limit of infinite reynolds numbers the method used is based on a symmetric form of the navier stokes equations stabilized with a galerkin least squares approach the proposed procedure provides appealing results it is as satisfactory as the use of germano and lilly s dynamic algorithm without stabilization flaws and at a lower cost comparisons between numerical dissipation and the proper subgrid closure show that the variational multiscale models tend to compute a turbulent viscosity that accounts for the numerical sources of dissipation which reveals an important feature for an intensive and robust use of vms large eddy simulation

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

a high order discontinuous galerkin method for unsteady advection diffusion problems abstract a high order discontinuous galerkin method with lagrange multipliers is presented for the solution of unsteady advection diffusion problems in the high peclet number regime it operates directly on the second order form of the governing equation and does not require any stabilization its spatial basis functions are chosen among the free space solutions of the homogeneous form of the partial differential equation obtained after time discretization it also features lagrange multipliers for enforcing a weak continuity of the approximated solution across the element interface boundaries this leads to a system of differential algebraic equations which are time integrated by an implicit family of schemes the numerical stability of these schemes and the well posedness of the overall discretization method are supported by a theoretical analysis the performance of this method is demonstrated for various high peclet number constant coefficient model flow problems

time dependent subgrid scales in residual based large eddy simulation of turbulent channel flow the present study investigates the effect of taking into account the time dependency of the fine subgrid scales in a residual based variational multiscale approach for large eddy simulation the residual based variational multiscale method with time dependent dynamic subgrid scales is presented and the impact of the time dependency is studied for the well known test case of turbulent channel flow results are presented from computations for various values of the reynolds number namely ret 180 ret 395 and ret 590 and several time step sizes a generalized a time integration scheme is employed results from our numerical experiments with dynamic subgrid scales are compared to results obtained with an approximation not explicitly taking the time dependency of the subgrid scales into account for all re t values and time step sizes under consideration results for resolved quantities computed by both approaches are very similar this statement applies to both mean streamwise velocity and root mean square velocity fluctuations however it provides a model for the subgrid scales not depend ing on the time step size and enabling a more robust representation of unresolved scales thus we conclude that the time dependent subgrid scale approximation is not capable of producing more accurate results for this type of flow if the time step size is chosen within an optimal range however we expect it to be more advantageous for more complex problems since our results indicate that it provides a more reliable representation of unresolved scales

mixed finite element methods with convection stabilization for the large eddy simulation of incompressible turbulent flows abstract the variational multiscale method thought as an implicit large eddy simulation model for turbulent flows has been shown to be an alternative to the widely used physical based models this method is traditionally combined with equal order velocity pressure pairs since it provides pressure stabilization in this work we consider a different approach based on inf sup stable elements and convection only stabilization in order to do so we consider a symmetric projection stabilization of the convective term using an orthogonal subscale decomposition the accuracy and efficiency of this method compared with residual based algebraic subgrid scales and orthogonal subscales methods for equal order interpolation is assessed in this paper moreover when inf sup stable elements are used the grad div stabilization term has been shown to be essential to guarantee accurate solutions hence a study of the influence of such term in the large eddy simulation of turbulent incompressible flows is also performed furthermore a recursive block preconditioning strategy has been considered for the resolution of the problem with an implicit treatment of the projection terms two different benchmark tests have been solved the taylor green vortex flow with r e 1600 and the turbulent channel flow at r e 395 and r e 590

an algebraic variational multiscale multigrid method based on plain aggregation for convection diffusion problems a new computational framework referred to as algebraic variational multiscale multigrid method is proposed representing the initial step of our work on merging the variational multiscale method with algebraic multigrid projection methods this new approach allows for a separation of resolved scales into various scale groups in a purely algebraic way that is with no need to utilize further discretizations beyond the basic one by this means it conveniently facilitates the application of modeling terms either to all scale groups or only to selected scale groups for instance only to the fine scales of the problem variational multigrid techniques form the basis of our new approach after presenting the cornerstones of the framework for an abstract problem formulation the close relationship of the variational multiscale method to projection methods in general and to variational multigrid techniques are discussed the algebraic variational multiscale multigrid method is then particularly analyzed for convection diffusion problems the present initial study focuses on exploiting the methodical aspects of the new framework by developing a fine scale discontinuity capturing approach to diminish oscillations at sharp layers our technique including a fine scale discontinuity capturing term is applied to numerical examples of strongly convection dominated convection diffusion problems the results demonstrate that it enables the diminuation of local oscillations at parabolic boundary and interior layers by about 60 80 percent without any notable smearing effect

a variational multiscale method for incompressible turbulent flows bubble functions and fine scale fields this paper presents a residual based turbulence model for the incompressible navier stokes equations the method is derived employing the variational multiscale vms framework a multiscale decomposition of the continuous solution and a priori unique decomposition of the admissible spaces of functions lead to two coupled nonlinear problems termed as the coarse scale and the fine scale sub problems the fine scale velocity field is assumed to be nonlinear and time dependent and is modeled via the bubble functions approach applied directly to the fine scale sub problem a significant contribution in this paper is a systematic and consistent derivation of the fine scale variational operator commonly termed as the stabilization tensor that possesses the right order in the advective and diffusive limits and variationally projects the fine scale solution onto the coarse scale space a direct treatment of the fine scale problem via bubble functions offers several fine scale approximation options with varying degrees of mathematical sophistication that are investigated via benchmark problems numerical accuracy of the proposed method is shown on a forced isotropic turbulence problem statistically stationary turbulent channel flow problems at ret 395 and 590 and non equilibrium turbulent flow around a cylinder at re 3 900