Volker John

A Finite Element Variational Multiscale Method for the Navier-Stokes Equations

This paper presents a variational multiscale method (VMS) for the incompressible Navier--Stokes equations which is defined by a large scale space LH for the velocity deformation tensor and a turbulent viscosity

On Finite Element Methods for 3D Time-Dependent Convection-Diffusion-Reaction Equations with Small Diffusion

\nu_T

A numerical study of a posteriori error estimators for convection–diffusion equations

. The connection of this method to the standard formulation of a VMS is explained. The conditions on LH under which the VMS can be implemented easily and efficiently into an existing finite element code for solving the Navier--Stokes equations are studied. Numerical tests with the Smagorinsky large eddy simulation model for

Finite element error analysis of a variational multiscale method for the Navier-Stokes equations

\nu_T

Slip with friction and penetration with resistance boundary conditions for the Navier--Stokes equations--numerical tests and aspects of the implementation

are presented.

Numerical performance of smoothers in coupled multigrid methods for the parallel solution of the incompressible Navier–Stokes equations

Article history: Received 14 May 2008 Received in revised form 25 August 2008 Accepted 28 August 2008 Available online 12 September 2008

Error Analysis of the SUPG Finite Element Discretization of Evolutionary Convection-Diffusion-Reaction Equations

This paper presents a numerical study of a posteriori error estimators for convection‐diAusion equations. The study involves the gradient indicator, an a posteriori error estimator which is based on gradient recovery, three residual-based error estimators for diAerent norms, and two error estimators which are defined by solutions of local Neumann problems. They are compared with respect to the reliable estimation of the global error and with respect to the accuracy of the computed solutions on adaptively refined grids. The numerical study shows for both criteria of comparison that none of the considered error estimators works satisfactorily in all tests. ” 2000 Elsevier Science S.A. All rights reserved. MSC: 65N50; 65N30

A Numerical Study of a Class of LES Models

The paper presents finite element error estimates of a variational multiscale method (VMS) for the incompressible Navier–Stokes equations. The constants in these estimates do not depend on the Reynolds number but on a reduced Reynolds number or on the mesh size of a coarse mesh.

The Commutation Error of the Space Averaged Navier-Stokes Equations on a Bounded Domain

We consider slip with friction and penetration with resistance boundary conditions in the steady state Navier-Stokes equations. This paper describes some aspects of the implementation of these boundary conditions for finite element discretizations. Numerical tests on two- and three-dimensional channel flows across a step using the slip with friction boundary condition study the influence of the friction parameter on the position of the reattachment point and the reattachment line of the recirculating vortex, respectively.

A streamline-diffusion method for nonconforming finite element approximations applied to convection-diffusion problems

In recent benchmark computations [Schafer M, Turek S. The benchmark problem ‘Flow around a cylinder’. In Flow Simulation with High-Performance Computers II, Hirschel EH (ed.), vol. 52 of Notes on Numerical Fluid Mechanics. Vieweg: Wiesbaden, 1996; 547–566], coupled multigrid methods have been proven as efficient solvers for the incompressible Navier–Stokes equations. A numerical study of two classes of smoothers in the framework of coupled multigrid methods is presented. The class of Vanka-type smoothers is characterized by the solution of small local linear systems of equations in a Gauss–Seidel manner in each smoothing step, whereas the Brass–Sarazin-type smoothers solve a large global saddle point problem. The behaviour of these smoothers with respect to computing times and parallel overheads is studied for two-dimensional steady state and time-dependent Navier–Stokes equations.