An Adaptive Refinement Ratio Algorithm for Structured AMR Method Based on SAMRAI Framework

In this paper, we present an adaptive refinement ratio algorithm for structured adaptive mesh refinement (SAMR) method based on SAMRAI framework. We developed our algorithm based on an example application program of SAMRAI framework, an AMR Euler gas dynamics application. The Euler class of this application provides routines for a sample application code that solves the Euler equations of gas dynamics. We first get the average error of each level in hierarchy from the process of error estimating, and determine the new refinement ratio for each level according to the average error of each level. Then, we apply the new refinement ratios when regridding time. After that, it is have to do some repairing work for the new patch hierarchy. From the numerical evaluation, we can see that, our algorithm can control the average errors of levels in hierarchy in an acceptable range and save calculation time when the initial refinement ratio is set to a high const value to catch smaller features of the application problem.