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

• Published in: International journal for numerical methods in fluids 2009-09, Vol.61 (1), p.1-22
• Main Authors: Lins, Erb F., Elias, Renato N., Guerra, Gabriel M., Rochinha, Fernando A., Coutinho, Alvaro L. G. A.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Computational methods in fluid dynamics; edge-based computations; Exact sciences and technology; Finite element method; Fluid dynamics; Fluid flow; Fundamental areas of phenomenology (including applications); large eddy simulation; Mathematical analysis; Mathematical models; Navier-Stokes equations; parallel computing; Physics; stabilized finite elements; Turbulence; Turbulence simulation and modeling; Turbulent flow; Turbulent flows, convection, and heat transfer; variational multiscale method
• ISSN: 0271-2091; 1097-0363; 1097-0363
• DOI: 10.1002/fld.1941

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.