Well-balanced unstaggered central schemes for the Euler equations with gravitation

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dc.contributor.author Touma, R.
dc.contributor.author Koley, U.
dc.contributor.author Kingenberg, C.
dc.date.accessioned 2018-09-07T13:19:48Z
dc.date.available 2018-09-07T13:19:48Z
dc.date.copyright 2016 en_US
dc.date.issued 2018-09-07
dc.identifier.issn 1095-7197 en_US
dc.identifier.uri http://hdl.handle.net/10725/8446
dc.description.abstract We consider the Euler equations with gravitational source term and propose a new well-balanced unstaggered central finite volume scheme, which can preserve the hydrostatic balance state exactly. The proposed scheme evolves a nonoscillatory numerical solution on a single grid, avoids the time consuming process of solving Riemann problems arising at the cell interfaces, and is second-order accurate both in time and space. Furthermore, the numerical scheme follows a well-balanced discretization that first discretizes the gravitational source term according to the discretization of the flux terms, and then mimics the surface gradient method and discretizes the density and energy according to the discretization of steady state density and energy functions, respectively. Finally, several numerical experiments demonstrating the performance of the well-balanced schemes in both one and two spatial dimensions are presented. The results indicate that the new scheme is accurate, simple, and robust. en_US
dc.language.iso en en_US
dc.title Well-balanced unstaggered central schemes for the Euler equations with gravitation en_US
dc.type Article en_US
dc.description.version Published en_US
dc.author.school SAS en_US
dc.author.idnumber 200502835 en_US
dc.author.department Computer Science and Mathematics en_US
dc.description.embargo N/A en_US
dc.relation.journal SIAM Journal on Scientific Computing en_US
dc.journal.volume 38 en_US
dc.journal.issue 5 en_US
dc.article.pages B773–B807 en_US
dc.keywords Euler equations en_US
dc.keywords Well-balanced unstagged central schemes en_US
dc.keywords Finite volume methods en_US
dc.keywords Gravitational field en_US
dc.identifier.doi https://doi.org/10.1137/140992667 en_US
dc.identifier.ctation Touma, R., Koley, U., & Klingenberg, C. (2016). Well-balanced unstaggered central schemes for the Euler equations with gravitation. SIAM Journal on Scientific Computing, 38(5), B773-B807. en_US
dc.author.email rony.touma@lau.edu.lb en_US
dc.identifier.tou http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php en_US
dc.identifier.url https://epubs.siam.org/doi/abs/10.1137/140992667 en_US
dc.author.affiliation Lebanese American University en_US

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