Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:355

Article

Di Pietro, Daniele A.¹  Marche, Fabien¹ 

[1] Univ Montpellier, IMAG, CNRS, F-34095 Montpellier, France

关键词: Green-Naghdi equations;    Discontinuous Galerkin;    Internal penalty methods;    High-order schemes;    Free surface flows;    Shallow water equations;    Dispersive equations;   

DOI  :  10.1016/j.jcp.2017.11.009

来源: Elsevier

【 摘 要 】

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 dispersive 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 consistent way. Similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dispersive models. These formulations are validated again several benchmarks involving h-convergence, p-convergence and comparisons with experimental data, showing optimal convergence properties. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free