Comparison of adaptive multiresolution and adaptive mesh refinement applied to simulations of the compressible Euler equations
This work provides a benchmark comparison of two adaptive methods for computational fluid dynamics, but the results are incremental and specific to the tested codes and test cases.
The paper compares adaptive multiresolution (MR) and adaptive mesh refinement (AMR) for solving compressible Euler equations, finding similar CPU time compression trends but MR offers better memory compression and slightly enhanced convergence, albeit with larger absolute overhead.
We present a detailed comparison between two adaptive numerical approaches to solve partial differential equations (PDEs), adaptive multiresolution (MR) and adaptive mesh refinement (AMR). Both discretizations are based on finite volumes in space with second order shock-capturing, and explicit time integration either with or without local time-stepping. The two methods are benchmarked for the compressible Euler equations in Cartesian geometry. As test cases a 2D Riemann problem, Lax-Liu 6, and a 3D ellipsoidally expanding shock wave have been chosen. We compare and assess their computational efficiency in terms of CPU time and memory requirements. We evaluate the accuracy by comparing the results of the adaptive computations with those obtained with the corresponding FV scheme using a regular fine mesh. We find that both approaches yield similar trends for CPU time compression for increasing number of refinement levels. MR exhibits more efficient memory compression than AMR and shows slightly enhanced convergence; however, a larger absolute overhead is measured for the tested codes.