A Comparison of Three Adaptive Finite Element Re nement Techniques for Incompressible Navier-Stokes Equations Using a CBS Scheme

Abstract

Abstract. The numerical solution of incompressible Navier-Stokes equations for ows involving complex geometries is greatly a ected by mesh resolution. In these ows, some regions may need ner mesh than others. Adaptive Mesh Re nement (AMR) techniques enable the mesh to be locally re ned, based on error distribution in the previous analysis. In this paper, three adaptive re nement methods, namely, Superconvergent Patch Recovery (SPR) based re nement, gradient based re nement and curvature (2nd derivative) based re nement are used in conjunction with the characteristic based split nite element method to solve a benchmark problem of a lid-driven cavity. The results of the proposed adaptive re nement methods are presented and their e ciencies are compared. The results show the e ectiveness of the adaptive re nement method for the e cient and accurate simulation of ow problems.