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.

Acknowledgments

The financial support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca).