Adaptive multiresolution or adaptive mesh refinement? A case study for 2D Euler equations

Abstract

Abstract We present adaptive multiresolution (MR) computations ofthe two-dimensional compressible Euler equations for a classicalRiemann problem. The results are then compared with respect to accuracyand computational efficiency, in terms of CPU time and memory requirements,with the corresponding finite volume scheme on a regular grid. Forthe same test case, we also perform computations using adaptive meshrefinement (AMR) imposing similar accuracy requirements. The resultsthus obtained are compared in terms of computational overhead andcompression of the computational grid, using in addition either localor global time stepping strategies. We preliminarily conclude thatthe multiresolution techniques yield improved memory compressionand gain in CPU time with respect to the adaptive mesh refinementmethod.