On thermodynamic consistency of generalised Lagrange multiplier magnetohydrodynamic solvers
On thermodynamic consistency of generalised Lagrange multiplier magnetohydrodynamic solvers
This work presents a new implementation of compressible magnetohydrodynamic (MHD) models in the context of the generalised Lagrange multiplier (GLM), combined with source term techniques to retain entropy stability, necessary for thermodynamic consistency. The GLM techniques introduce a scalar field, that is evolved along the MHD quantities, in order to aid in an error control of ∇ ⋅ B. Our implementation employs second-order HLL-type schemes in finite-volume form and an explicit time discretisation in a parallel framework. We furthermore revise and develop different GLM–MHD and source term approaches as sit-on-top solvers, that can be added to existing MHD applications. It is shown that Galilean invariance is a major factor determining the capacity of these solvers to control ∇ ⋅ B, as achieved in GLM–MHD systems with Powell source terms. Moreover, it also influences the physical robustness of the solver, in particular its ability to maintain positive pressure during the simulation. In addition, we show that our new and easily reproducible implementation is entropy consistent.
divergence cleaning, entropy stability, galilean invariance, numerical simulation, space physics, Space physics, Entropy stability, Numerical simulation, Galilean invariance, Divergence cleaning
Sattler Cassara, Leonardo
27e46f11-3c8d-47e2-89d1-69beca564a98
Moreira Souza Lopes, Muller
ac3efdac-469b-4129-a236-6693ce7ee5ee
Domingues, Margarete Oliveira
393cd03f-2ee9-482c-9c72-1988aef9b05f
Mendes, Odim
1a4cca69-9c5b-4b00-ab25-e85450116b7b
Deiterding, Ralf
ce02244b-6651-47e3-8325-2c0a0c9c6314
20 June 2023
Sattler Cassara, Leonardo
27e46f11-3c8d-47e2-89d1-69beca564a98
Moreira Souza Lopes, Muller
ac3efdac-469b-4129-a236-6693ce7ee5ee
Domingues, Margarete Oliveira
393cd03f-2ee9-482c-9c72-1988aef9b05f
Mendes, Odim
1a4cca69-9c5b-4b00-ab25-e85450116b7b
Deiterding, Ralf
ce02244b-6651-47e3-8325-2c0a0c9c6314
Sattler Cassara, Leonardo, Moreira Souza Lopes, Muller, Domingues, Margarete Oliveira, Mendes, Odim and Deiterding, Ralf
(2023)
On thermodynamic consistency of generalised Lagrange multiplier magnetohydrodynamic solvers.
Computational and Applied Mathematics, 42 (5), [223].
(doi:10.1007/s40314-023-02338-2).
Abstract
This work presents a new implementation of compressible magnetohydrodynamic (MHD) models in the context of the generalised Lagrange multiplier (GLM), combined with source term techniques to retain entropy stability, necessary for thermodynamic consistency. The GLM techniques introduce a scalar field, that is evolved along the MHD quantities, in order to aid in an error control of ∇ ⋅ B. Our implementation employs second-order HLL-type schemes in finite-volume form and an explicit time discretisation in a parallel framework. We furthermore revise and develop different GLM–MHD and source term approaches as sit-on-top solvers, that can be added to existing MHD applications. It is shown that Galilean invariance is a major factor determining the capacity of these solvers to control ∇ ⋅ B, as achieved in GLM–MHD systems with Powell source terms. Moreover, it also influences the physical robustness of the solver, in particular its ability to maintain positive pressure during the simulation. In addition, we show that our new and easily reproducible implementation is entropy consistent.
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Accepted/In Press date: 15 June 2023
Published date: 20 June 2023
Additional Information:
Funding Information:
This work is supported by Grants from CNPq (306985/2021-7, 140563/2020-2, 13429/2022-7 and 400077/2022-1), and FAPESP (2020/13015-0), and takes part of the development of INPE-TAP-SEI 01340.003199/2021-72 and 01340.003098/2021-00. We are grateful to V. E. Menconni (PCI 313429/2022-7) for their helpful computational assistance. The authors thank all free(dom)-software including VisIt (Childs et al. ).
Funding Information:
MML received from PNPD-CAP-INPE/CAPES a scholarship, and LSC from CNPq Grant 140563/2020-2, MOD from CNPq Grant 306985/2021-7, and MCTI/PCI-INPE/CNPq 140563/2020-2, 13429/2022-7, 400077/2022-1, and Fapesp 2020/13015-0.
Publisher Copyright:
© 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.
Keywords:
divergence cleaning, entropy stability, galilean invariance, numerical simulation, space physics, Space physics, Entropy stability, Numerical simulation, Galilean invariance, Divergence cleaning
Identifiers
Local EPrints ID: 478412
URI: http://eprints.soton.ac.uk/id/eprint/478412
ISSN: 2238-3603
PURE UUID: 6d2bee1a-2439-4e59-bed9-2d85ecad5610
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Date deposited: 30 Jun 2023 16:36
Last modified: 17 Mar 2024 03:39
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Contributors
Author:
Leonardo Sattler Cassara
Author:
Muller Moreira Souza Lopes
Author:
Margarete Oliveira Domingues
Author:
Odim Mendes
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