A Simple and Efficient Isotropic Mesh Adaptation Scheme Based on Control-Volume Flux Imbalance

Abstract

The primary goal of this work is to develop a simple residual-based error indicator in the context of the finite-volume method that is as easy to use as conventional gradient-based error indicators and as robust as residual-based error indicators. The residual is defined as the cell imbalance error or rather the net flow error across the faces of each control-volume. To estimate the residual, the neglected Taylor series terms in the discretization of the face flows are used. Then a simplified residual-based error indicator suitable for isotropic triangular meshes is developed. A mesh adaptation scheme is used to minimize the global value of the error indicator through local refinement, coarsening, and vertex repositioning. The adaptation results for the lid-driven cavity flow at Re = 1,600 and the impinging slot jet flow at Re = 500 confirm that the proposed adaptation scheme can effectively decrease the discretization error by an order of magnitude in fewer than 10 iterations.