Numerical approximation of a multiscale Leray model for incompressible, viscous flow
Abigail L. Bowers · Contemporary mathematics - American Mathematical Society · 2013
This article develops, analyzes and tests a finite element method for approximating solutions to the Leray- α \alpha model, where the filtering is performed on a finer mesh than the momentum/mass system. Typical simulations with Leray- α \alpha can oversmooth solutions, and our algorithm is proposed to help avoid this potential drawback. We prove the proposed scheme is unconditionally stable and optimally convergent, with choice of element order and fine mesh width guided by the analysis. A complete and rigorous numerical analysis of the scheme is given, along with experiments that demonstrate its effectiveness.