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dc.contributor.authorChen, Fang
dc.contributor.authorSamtaney, Ravi
dc.date.accessioned2021-09-12T13:09:27Z
dc.date.available2021-09-12T13:09:27Z
dc.date.issued2021-09-10
dc.identifier.citationChen, F., & Samtaney, R. (2021). A numerical method for self-similar solutions of the ideal magnetohydrodynamics. Journal of Computational Physics, 110690. doi:10.1016/j.jcp.2021.110690
dc.identifier.issn0021-9991
dc.identifier.doi10.1016/j.jcp.2021.110690
dc.identifier.urihttp://hdl.handle.net/10754/671151
dc.description.abstractWe present a numerical method to obtain self-similar solutions of the ideal magnetohydrodynamics (MHD) equations. Under a self-similar transformation, the initial value problem (IVP) is converted into a boundary value prob1 lem (BVP) by eliminating time and transforming the system to self-similar coordinates (ξ ≡ x/t, η ≡ y/t). The ideal MHD system of equations is augmented by a generalized Lagrange multiplier (GLM) to maintain the solenoidal condition on the magnetic field. The self-similar solution to the BVP is solved using an iterative method, and implemented using the p4est adaptive mesh refinement (AMR) framework. Existing Riemann solvers (e.g., Roe, HLLD etc.) can be modified in a relatively straightforward manner and used in the present method. Numerical tests numerical tests illustrate that the present self-similar solution to the BVP exhibits sharper discontinuities than the corresponding one solved by the IVP. We compare and contrast the IVP and BVP solutions in several one dimensional shock-tube test problem and two dimensional test cases include shock wave refraction at a contact discontinuity, reflection at a solid wall, and shock wave diffraction over a right angle corner.
dc.description.sponsorshipThe research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST) under grant no. BAS/1/1349-01-01.
dc.publisherElsevier BV
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S0021999121005854
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Physics, [, , (2021-09-10)] DOI: 10.1016/j.jcp.2021.110690 . © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleA numerical method for self-similar solutions of the ideal magnetohydrodynamics
dc.typeArticle
dc.contributor.departmentFluid and Plasma Simulation Group (FPS)
dc.contributor.departmentMechanical Engineering Program
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalJournal of Computational Physics
dc.rights.embargodate2023-09-10
dc.eprint.versionPost-print
dc.identifier.pages110690
kaust.personChen, Fang
kaust.personSamtaney, Ravi
kaust.grant.numberBAS/1/1349-01-01
dc.date.accepted2021-09-10
refterms.dateFOA2021-09-12T13:13:41Z
kaust.acknowledged.supportUnitBAS
dc.date.published-online2021-09-10
dc.date.published-print2021-12


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