Residual Least-Squares Error Estimate for Unstructured h-Adaptive Meshes

Abstract

An a posteriori error estimate suitable for finite-volume adaptive computations is presented. The error estimate combines the least-squares method regressions with the residual computation, which provides information from the grid quality and the governing equations for a better local adaptation of the unstructured grid. The decision algorithm uses the information provided by the error estimate and does not require problem-dependent constants; it also uses a grid interface correction step to provide a smoother and a high-quality adaptive grid. The proposed error estimate and the adaptive refinement algorithm are verified against analytic solution for different two-dimensional problems. In addition, calculations of three-dimensional laminar flows with different types of unstructured grids have demonstrated the applicability of the adaptive method.