A Relaxation Method for Modeling Two-Phase Shallow Granular Flows

Abstract : We present a relaxation approach for the numerical solution of a depth-averaged two-phase model describing the flow of a shallow layer of a mixture of solid granular material and fluid. A relaxation model is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original system. These new variables are governed by linear equations with coefficients that determine the eigenvalues of the relaxation model. The proposed relaxation strategy results in the definition of a particular approximate Riemann solver for the original model equations. Compared to a Roe-type Riemann solver that we have proposed in previous work, the new solver has the advantage of a certain degree of freedom in the specification of the wave speeds through the choice of the relaxation parameters. This flexibility can be exploited to obtain a more robust method than the Roe type one in the treatment of wet/dry fronts. Some numerical experiments are presented to show the effectiveness of the proposed approach.
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Conference papers
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Contributor : Marica Pelanti <>
Submitted on : Thursday, July 7, 2016 - 10:38:48 AM
Last modification on : Wednesday, July 3, 2019 - 10:48:05 AM

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Marica Pelanti, François Bouchut. A Relaxation Method for Modeling Two-Phase Shallow Granular Flows. Proceedings of the Twelfth International Conference on Hyperbolic Problems, 2008, College Park, United States. pp. 835-844. ⟨hal-01342943⟩

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