Central finite volume methods with constrained transport divergence treatment for ideal MHD

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dc.contributor.author Touma, R.
dc.contributor.author Arminjon, Paul
dc.date.accessioned 2016-04-07T09:09:15Z
dc.date.available 2016-04-07T09:09:15Z
dc.date.copyright 2005
dc.date.issued 2016-04-07
dc.identifier.issn 0021-9991 en_US
dc.identifier.uri http://hdl.handle.net/10725/3509
dc.description.abstract Two and three-dimensional finite volume extensions of the Lax–Friedrichs (LF) and Nessyahu–Tadmor one-dimensional difference schemes were previously presented and successfully applied to several problems for nonlinear hyperbolic systems, and in particular to typical test cases for both inviscid and viscous compressible flows. These “central” schemes by-pass the resolution, at the cell interfaces, of the Riemann problems, thanks to the use of the staggered LF scheme which serves as the base scheme on which high order finite volume methods can be constructed using van Leer’s MUSCL-type limited reconstruction principle. For this purpose, two dual grids are used at alternate time steps. These methods are extended here to several problems in one- and multi-dimensional ideal compressible magnetohydrodynamics using a modified version of the first author’s central methods with oblique (diamond shaped) dual cells. In two-dimensions the system has eight equations and solving the corresponding Riemann problem is an elaborate and time-consuming process. Central methods lead to significant computing time reductions, and the numerical experiments presented here suggest the accuracy is quite satisfactory. In order to satisfy the physical constraint ∇ · B = 0, we have constructed a strategy (“CTCS”) inspired from the Constrained Transport method of Evans and Hawley. The validity of our base scheme and our CTCS approach is clearly confirmed by the results. en_US
dc.language.iso en en_US
dc.title Central finite volume methods with constrained transport divergence treatment for ideal MHD en_US
dc.type Article en_US
dc.description.version Published en_US
dc.author.school SAS en_US
dc.author.idnumber 200502935 en_US
dc.author.woa N/A en_US
dc.author.department Computer Science and Mathematics en_US
dc.description.embargo N/A en_US
dc.relation.journal Journal of Computational Physics en_US
dc.journal.volume 204 en_US
dc.journal.issue 2 en_US
dc.article.pages 737-759 en_US
dc.keywords Numerical methods en_US
dc.keywords Magnetohydrodynamics en_US
dc.keywords Central schemes en_US
dc.keywords Non-oscillatory en_US
dc.identifier.doi http://dx.doi.org/10.1016/j.jcp.2004.10.034 en_US
dc.identifier.ctation Arminjon, P., & Touma, R. (2005). Central finite volume methods with constrained transport divergence treatment for ideal MHD. Journal of Computational Physics, 204(2), 737-759. en_US
dc.author.email rony.touma@lau.edu.lb
dc.identifier.url http://www.sciencedirect.com/science/article/pii/S002199910400436X

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