Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
We present the results from verification and convergence analysis of adaptive mesh refinement (AMR) calculations for two different AMR codes. Code verification is extremely important for science-based prediction and simulation. Previous verification efforts focused on the convergence behavior of uniform grid. With AMR, we can obtain more accurate results with substantially less computational cost. The ideal goal of AMR is to achieve the same accuracy in the refinement region as in the corresponding fine uniform grid. However, test results shows that AMR may not achieve the convergence of the equivalent finest uniform grid. In some cases, numerical results with AMR have even larger error than those without AMR. AMR can also trigger an instability for some applications.
