Derivation of the non-linear shallow water equations over unsaturated porous media: a discontinuous galerkin method for coarse-grained beaches - Institut de mathématiques de Toulon
Pré-Publication, Document De Travail Année : 2024

Derivation of the non-linear shallow water equations over unsaturated porous media: a discontinuous galerkin method for coarse-grained beaches

Résumé

This work will consider the physics of free-surface flow and groundwa- ter flow in a coupled model. Coupled models of such phenomena are not clearly justified, and there is a lack of precision in deriving such a model. The primary aim of this work is to derive a coupled model of Shallow Wa- ter Equations (SWE) and Richards’ Equation (RE) using asymptotic con- siderations. The numerical coupling chosen for the unified model will be explained as a parallel coupling. Additionally, numerical considerations on how to solve this model using Discontinuous Galerkin (DG) methods will be provided. Furthermore, explanations will be given about how informa- tion is exchanged between the two models, which are time-synchronized. The solution of RE coupled with SWE using the mentioned procedure with DG formulation is implemented in RIVAGE (an in-house numerical code based on discontinuous Galerkin method), which is then tested on a numerical problem and validated against an experimental benchmark.
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Dates et versions

hal-04713029 , version 1 (28-09-2024)

Identifiants

  • HAL Id : hal-04713029 , version 1

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Camille Poussel, Mehmet Ersoy, Frederic Golay, Damien Sous. Derivation of the non-linear shallow water equations over unsaturated porous media: a discontinuous galerkin method for coarse-grained beaches. 2024. ⟨hal-04713029⟩
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