Central finite volume schemes on nonuniform grids and applications

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dc.contributor.author Touma, R.
dc.contributor.author Habre, S.
dc.contributor.author Zeidan, D.
dc.date.accessioned 2015-09-14T08:20:28Z
dc.date.available 2015-09-14T08:20:28Z
dc.date.copyright 2015-07
dc.date.issued 2017-04-07
dc.identifier.issn 0096-3003 en_US
dc.identifier.uri http://hdl.handle.net/10725/2137
dc.description.abstract We propose a new one-dimensional unstaggered central scheme on nonuniform grids for the numerical solution of homogeneous hyperbolic systems of conservation laws with applications in two-phase flows and in hydrodynamics with and without gravitational effect. The numerical base scheme is a generalization of the original Lax–Friedrichs scheme and an extension of the Nessyahu and Tadmor central scheme to the case of nonuniform irregular grids. The main feature that characterizes the proposed scheme is its simplicity and versatility. In fact, the developed scheme evolves a piecewise linear numerical solution defined at the cell centers of a nonuniform grid, and avoids the resolution of the Riemann problems arising at the cell interfaces, thanks to a layer of staggered cells used intermediately. Spurious oscillations are avoided using a slopes limiting procedure. The developed scheme is then validated and used to solve classical problems arising in gas–solid two phase flow problems. The proposed scheme is then extended to the case of non-homogenous hyperbolic systems with a source term, in particular to the case of Euler equations with a gravitational source term. The obtained numerical results are in perfect agreement with corresponding ones appearing in the recent literature, thus confirming the efficiency and potential of the proposed method to handle both homogeneous and non-homogeneous hyperbolic systems. en_US
dc.language.iso en en_US
dc.title Central finite volume schemes on nonuniform grids and applications en_US
dc.type Article en_US
dc.description.version Published en_US
dc.author.school SAS en_US
dc.author.woa N/A en_US
dc.author.department Mathematics en_US
dc.description.embargo N/A en_US
dc.relation.journal Applied Mathematics and Computation en_US
dc.journal.volume 262 en_US
dc.article.pages 15-30 en_US
dc.identifier.doi http://dx.doi.org/10.1016/j.amc.2015.03.129 en_US
dc.identifier.ctation Touma, R., Zeidan, D., & Habre, S. (2015). Central finite volume schemes on nonuniform grids and applications. Applied Mathematics and Computation, 262, 15-30. en_US
dc.author.email rony.touma@lau.edu.lb
dc.author.email shabre@lau.edu.lb
dc.identifier.url http://www.sciencedirect.com/science/article/pii/S0096300315004488

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