Weighted Interior Penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows

Abstract : In this paper, we further investigate the use of a fully discontinuous Finite Element discrete formulation for the study of shallow water free surface flows in the fully nonlinear and weakly dis-persive flow regime. We consider a decoupling strategy in which we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non-hydrostatic effects. This source term can be computed through the resolution of elliptic second-order linear sub-problems, which only involve second order partial derivatives in space. We then introduce an associated Symmetric Weighted Internal Penalty discrete bilinear form, allowing to deal with the discontinuous nature of the elliptic problem's coefficients in a stable and consistant way. Similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dis-persive models. These formulations are validated again several benchmarks involving h-convergence, p-convergence and comparisons with experimental data, showing optimal convergence properties.
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Journal of Computational Physics, Elsevier, 2018, 355, pp.285-309. 〈10.1016/j.jcp.2017.11.009〉
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Soumis le : jeudi 9 novembre 2017 - 09:47:39
Dernière modification le : mercredi 12 décembre 2018 - 15:27:56

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Daniele Di Pietro, Fabien Marche. Weighted Interior Penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows. Journal of Computational Physics, Elsevier, 2018, 355, pp.285-309. 〈10.1016/j.jcp.2017.11.009〉. 〈hal-01566446v2〉

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