Edge‐based finite element implementation of the residual‐based variational multiscale method

Abstract

Abstract In this work we extend our edge‐based stabilized finite element incompressible flow solver to turbulence modeling with the residual‐based variational multiscale (RB‐VMS) method. Using the advective‐form of the convection term of the Navier–Stokes equations, RB‐VMS is implemented as a straightforward extension of standard stabilized methods with a modified advective velocity. This requires minimum modification of the existing highly optimized code. Two test cases were solved to assess accuracy and performance of the present implementation. First, the laminar incompressible flow past a circular cylinder at Re = 100 and second, the fully turbulent incompressible flow in a lid‐driven cubic cavity at Re = 12000. Comparisons were made with standard stabilized finite element formulations, highly resolved numerical simulations and experimental data. Results have shown that the present implementation is able to achieve reasonable accuracy without performance degradation in different flow regimes. Copyright © 2008 John Wiley & Sons, Ltd.