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M. Moreira Lopes¹, R. Deiterding², M.O. Domingues¹ and O. Mendes³

¹Associate Laboratory of Applied Computing and Mathematics National Institute for Space Research, São José dos Campos Brazil
²Aerodynamics and Flight Mechanics Research Group University of Southampton, United Kingdom
³Space Geophysics Division, National Institute for Space Research, São José dos Campos Brazil

doi:10.4203/ccc.2.2.8

M. Moreira Lopes, R. Deiterding, M.O. Domingues, O. Mendes, "A Computationally Efficient Hybrid Magnetic Field Correction for the Magnetohydrodynamic Equations", in B.H.V. Topping, P. Iványi, (Editors), "Proceedings of the Eleventh International Conference on Engineering Computational Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 2, Paper 2.8, 2022, doi:10.4203/ccc.2.2.8

Keywords: adaptive mesh refinement, magnetohydrodynamics, high performance computing, divergence cleaning.

Abstract

During the simulations of the magnetohydrodynamic equations, numerical errors might cause the formation of non-physical divergence components in the magnetic field. This divergence compromises the stability and accuracy of the simulations. In order to overcome this problem, several methodologies, called divergence cleaning methods, are proposed. Besides many comparative works between these methods, the construction of the best approach is still an open problem. A popular divergence cleaning strategy is the parabolic-hyperbolic approach due to its easy implementation and low computational cost in CPU time, however this approach just transports and diffuses the divergence components instead of eliminating them globally. On the other hand, the elliptic approach, also known as the projection method, uses a Poisson equation to eliminate the divergence effectively at a huge computational cost. This work proposes a successful combination of these approaches in order to create a new divergence cleaning methodology that incorporates the advantages provided by both methods, a small CPU time and a good accuracy.

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Front Page Browse CCC CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Conferences ISSN 2753-3239 CCC: 2 PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping and P. Iványi Paper 2.8 A Computationally Efficient Hybrid Magnetic Field Correction for the Magnetohydrodynamic Equations M. Moreira Lopes¹, R. Deiterding², M.O. Domingues¹ and O. Mendes³ ¹Associate Laboratory of Applied Computing and Mathematics National Institute for Space Research, São José dos Campos Brazil ²Aerodynamics and Flight Mechanics Research Group University of Southampton, United Kingdom ³Space Geophysics Division, National Institute for Space Research, São José dos Campos Brazil doi:10.4203/ccc.2.2.8 Full Bibliographic Reference for this paper M. Moreira Lopes, R. Deiterding, M.O. Domingues, O. Mendes, "A Computationally Efficient Hybrid Magnetic Field Correction for the Magnetohydrodynamic Equations", in B.H.V. Topping, P. Iványi, (Editors), "Proceedings of the Eleventh International Conference on Engineering Computational Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 2, Paper 2.8, 2022, doi:10.4203/ccc.2.2.8 Keywords: adaptive mesh refinement, magnetohydrodynamics, high performance computing, divergence cleaning. Abstract During the simulations of the magnetohydrodynamic equations, numerical errors might cause the formation of non-physical divergence components in the magnetic field. This divergence compromises the stability and accuracy of the simulations. In order to overcome this problem, several methodologies, called divergence cleaning methods, are proposed. Besides many comparative works between these methods, the construction of the best approach is still an open problem. A popular divergence cleaning strategy is the parabolic-hyperbolic approach due to its easy implementation and low computational cost in CPU time, however this approach just transports and diffuses the divergence components instead of eliminating them globally. On the other hand, the elliptic approach, also known as the projection method, uses a Poisson equation to eliminate the divergence effectively at a huge computational cost. This work proposes a successful combination of these approaches in order to create a new divergence cleaning methodology that incorporates the advantages provided by both methods, a small CPU time and a good accuracy. download the full-text of this paper (PDF, 8 pages, 346 Kb) go to the previous paper go to the next paper return to the table of contents return to the volume description
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