Two-dimensional central-upwind schemes for curvilinear grids and application to gas dynamics with angular momentum

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Two-dimensional central-upwind schemes for curvilinear grids and application to gas dynamics with angular momentum

Article history: Received 30 April 2008 Received in revised form 17 February 2009 Accepted 27 July 2009 Available online 30 July 2009 MSC: 65M70 76M12 76U05

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We derive a second-order semi-discrete central-upwind scheme for oneand two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is wellbalanced in the sense that stationary steady-state solutions are exactly preserved by the scheme, and positivity preserving, that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new te...

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Compressible Two-phase Flows by Central and Upwind Schemes

This paper concerns numerical methods for two-phase flows. The governing equations are the compressible 2-velocity, 2-pressure flow model. Pressure and velocity relaxation are included as source terms. Results obtained by a Godunov-type central scheme and a Roe-type upwind scheme are presented. Issues of preservation of pressure equilibrium, and positivity of the partial densities are addressed...

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ژورنال

عنوان ژورنال: Computer Physics Communications

سال: 2009

ISSN: 0010-4655

DOI: 10.1016/j.cpc.2009.07.016