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<p>In this paper, a high order asymptotic preserving scheme is proposed for the two-dimensional nonlinear shallow water equations with Coriolis forces in all full Froude number regime. In this scheme, the original equations are firstly split into linear stiff parts and nonlinear non-stiff parts. Then an implicit-explicit Runge-Kutta discontinuous Galerkin method is proposed for solving the equations, in which the linear stiff parts are solved implicitly and the nonlinear non-stiff parts are solved explicitly. We formally prove that the proposed scheme is asymptotic preserving. Finally, several numerical examples are provided to demonstrate the effectiveness of our proposed scheme.</p>

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Numerical simulations of the shallow water equations with Coriolis forces in full Froude number by an asymptotic preserving DG scheme

  • 期刊论文

  • 发表日期：

    2025年5月14日

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  • Xian Xie,
  • Haiyun Dong,
  • Maojun Li

摘要

In this paper, a high order asymptotic preserving scheme is proposed for the two-dimensional nonlinear shallow water equations with Coriolis forces in all full Froude number regime. In this scheme, the original equations are firstly split into linear stiff parts and nonlinear non-stiff parts. Then an implicit-explicit Runge-Kutta discontinuous Galerkin method is proposed for solving the equations, in which the linear stiff parts are solved implicitly and the nonlinear non-stiff parts are solved explicitly. We formally prove that the proposed scheme is asymptotic preserving. Finally, several numerical examples are provided to demonstrate the effectiveness of our proposed scheme.