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Comparison of adaptive multiresolution and adaptive mesh refinement applied to simulations of the compressible Euler equations. (English) Zbl 1457.65069
Summary: We present a detailed comparison between two adaptive numerical approaches to solve partial differential equations, 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 two-dimensional Riemann problem, Lax-Liu $$\#6$$, and a three-dimensional 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.
Reviewer: Reviewer (Berlin)

##### MSC:
 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 65N08 Finite volume methods for boundary value problems involving PDEs 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65Y20 Complexity and performance of numerical algorithms 76L05 Shock waves and blast waves in fluid mechanics 76N06 Compressible Navier-Stokes equations 76M12 Finite volume methods applied to problems in fluid mechanics 35Q31 Euler equations
##### Software:
AMRCLAW; AMROC; AUSM; PARAMESH; Peano; VTF
Full Text:
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