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Multiresolution analysis as a criterion for effective dynamic mesh adaptation: A case study for Euler equations in the SAMR framework AMROC

Multiresolution analysis as a criterion for effective dynamic mesh adaptation: A case study for Euler equations in the SAMR framework AMROC
Multiresolution analysis as a criterion for effective dynamic mesh adaptation: A case study for Euler equations in the SAMR framework AMROC
Dynamic mesh adaptation methods require suitable refinement indicators. In the absence of a comprehensive error estimation theory, adaptive mesh refinement (AMR) for nonlinear hyperbolic conservation laws, e.g. compressible Euler equations, in practice utilizes mainly heuristic smoothness indicators like combinations of scaled gradient criteria. As an alternative, we describe in detail an easy to implement and computationally inexpensive criterion built on a two-level wavelet transform that applies projection and prediction operators from multiresolution analysis. The core idea is the use of the amplitude of the wavelet coefficients as smoothness indicator, as it can be related to the local regularity of the solution. Implemented within the fully parallelized and structured adaptive mesh refinement (SAMR) software system AMROC (Adaptive Mesh Refinement in Object-oriented C++), the proposed criterion is tested and comprehensively compared to results obtained by applying the scaled gradient approach. A rigorous quantification technique in terms of numerical adaptation error versus used finite volume cells is developed and applied to study typical two- and three-dimensional problems from compressible gas dynamics. It is found that the proposed multiresolution approach is considerably more efficient and also identifies - besides discontinuous shock and contact waves - in particular smooth rarefaction waves and their interaction as well as small-scale disturbances much more reliably. Aside from pathological cases consisting solely of planar shock waves, the majority of realistic cases show reductions in the number of used finite volume cells between 20 to 40%, while the numerical error remains basically unaltered.
AMROC, Block-structured parallel adaptive mesh refinement, adaptation criteria, compressible Euler equations, multiresolution analysis, wavelets
0045-7930
Deiterding, Ralf
ce02244b-6651-47e3-8325-2c0a0c9c6314
Domingues, Margarete O.
393cd03f-2ee9-482c-9c72-1988aef9b05f
Schneider, Kai
1db9f4c2-3835-4d02-837a-3be8932434f3
Deiterding, Ralf
ce02244b-6651-47e3-8325-2c0a0c9c6314
Domingues, Margarete O.
393cd03f-2ee9-482c-9c72-1988aef9b05f
Schneider, Kai
1db9f4c2-3835-4d02-837a-3be8932434f3

Deiterding, Ralf, Domingues, Margarete O. and Schneider, Kai (2020) Multiresolution analysis as a criterion for effective dynamic mesh adaptation: A case study for Euler equations in the SAMR framework AMROC. Computers & Fluids, 205, [104583]. (doi:10.1016/j.compfluid.2020.104583).

Record type: Article

Abstract

Dynamic mesh adaptation methods require suitable refinement indicators. In the absence of a comprehensive error estimation theory, adaptive mesh refinement (AMR) for nonlinear hyperbolic conservation laws, e.g. compressible Euler equations, in practice utilizes mainly heuristic smoothness indicators like combinations of scaled gradient criteria. As an alternative, we describe in detail an easy to implement and computationally inexpensive criterion built on a two-level wavelet transform that applies projection and prediction operators from multiresolution analysis. The core idea is the use of the amplitude of the wavelet coefficients as smoothness indicator, as it can be related to the local regularity of the solution. Implemented within the fully parallelized and structured adaptive mesh refinement (SAMR) software system AMROC (Adaptive Mesh Refinement in Object-oriented C++), the proposed criterion is tested and comprehensively compared to results obtained by applying the scaled gradient approach. A rigorous quantification technique in terms of numerical adaptation error versus used finite volume cells is developed and applied to study typical two- and three-dimensional problems from compressible gas dynamics. It is found that the proposed multiresolution approach is considerably more efficient and also identifies - besides discontinuous shock and contact waves - in particular smooth rarefaction waves and their interaction as well as small-scale disturbances much more reliably. Aside from pathological cases consisting solely of planar shock waves, the majority of realistic cases show reductions in the number of used finite volume cells between 20 to 40%, while the numerical error remains basically unaltered.

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Accepted/In Press date: 11 May 2020
e-pub ahead of print date: 15 May 2020
Published date: 15 June 2020
Keywords: AMROC, Block-structured parallel adaptive mesh refinement, adaptation criteria, compressible Euler equations, multiresolution analysis, wavelets

Identifiers

Local EPrints ID: 441015
URI: http://eprints.soton.ac.uk/id/eprint/441015
ISSN: 0045-7930
PURE UUID: 65dad4bf-c0df-4fc3-8c8f-351c6aefc1b1
ORCID for Ralf Deiterding: ORCID iD orcid.org/0000-0003-4776-8183

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Date deposited: 27 May 2020 16:55
Last modified: 28 Apr 2022 04:35

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Contributors

Author: Ralf Deiterding ORCID iD
Author: Margarete O. Domingues
Author: Kai Schneider

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