Comparison of adaptive multiresolution and adaptive mesh refinement applied to simulations of the compressible Euler equations
Comparison of adaptive multiresolution and adaptive mesh refinement applied to simulations of the compressible Euler equations
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.
S173-S193
Deiterding, Ralf
ce02244b-6651-47e3-8325-2c0a0c9c6314
Domingues, Margarete O.
393cd03f-2ee9-482c-9c72-1988aef9b05f
Gomes, Sonia M.
bfb3dbc0-56f3-4d44-a04c-70179e1ca027
Schneider, Kai
1db9f4c2-3835-4d02-837a-3be8932434f3
27 October 2016
Deiterding, Ralf
ce02244b-6651-47e3-8325-2c0a0c9c6314
Domingues, Margarete O.
393cd03f-2ee9-482c-9c72-1988aef9b05f
Gomes, Sonia M.
bfb3dbc0-56f3-4d44-a04c-70179e1ca027
Schneider, Kai
1db9f4c2-3835-4d02-837a-3be8932434f3
Deiterding, Ralf, Domingues, Margarete O., Gomes, Sonia M. and Schneider, Kai
(2016)
Comparison of adaptive multiresolution and adaptive mesh refinement applied to simulations of the compressible Euler equations.
SIAM Journal on Scientific Computing, 38 (5), .
(doi:10.1137/15M1026043).
Abstract
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.
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Accepted/In Press date: 7 March 2016
Published date: 27 October 2016
Organisations:
Aerodynamics & Flight Mechanics Group
Identifiers
Local EPrints ID: 389850
URI: http://eprints.soton.ac.uk/id/eprint/389850
ISSN: 1064-8275
PURE UUID: 5c351d3b-6f40-4f18-8266-89e81f59ad43
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Date deposited: 17 Mar 2016 10:09
Last modified: 15 Mar 2024 03:52
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Contributors
Author:
Margarete O. Domingues
Author:
Sonia M. Gomes
Author:
Kai Schneider
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