2003/06/02 by R. Keppens, Rony Keppens, Margreet Nool +4 · 6 citations
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #astro-ph
paper · pdf · doi:10.1016/s0010-4655(03)00139-5
published as Comput.Phys.Commun. 153 (2003) 317 · Published in Computer Physics Communications, figures absent due to file sizes, complete version at http://www.phys.uu.nl/~toth/
openalex publication_date 2003/06/02 · arxiv created 2004/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Obtainable computational efficiency is evaluated when using an Adaptive Mesh Refinement (AMR) strategy in time accurate simulations governed by sets of conservation laws. For a variety of 1D, 2D, and 3D hydro- and magnetohydrodynamic simulations, AMR is used in combination with several shock-capturing, conservative discretization schemes. Solution accuracy and execution times are compared with static grid simulations at the corresponding high resolution and time spent on AMR overhead is reported. Our examples reach corresponding efficiencies of 5 to 20 in multidimensional calculations and only 1.5 -- 8 % overhead is observed. For AMR calculations of multi-dimensional magnetohydrodynamic problems, several strategies for controlling the ∇ ⋅ \BB =0 constraint are examined. Three source term approaches suitable for cell-centered \BB representations are shown to be effective. For 2D and 3D calculations where a transition to a more globally turbulent state takes place, it is advocated to use an approximate Riemann solver based discretization at the highest allowed level(s), in combination with the robust Total Variation Diminishing Lax-Friedrichs method on the coarser levels. This level-dependent use of the spatial discretization acts as a computationally efficient, hybrid scheme.