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<p>In this study we present a pseudospectral scheme for solving shallow water equations on a spherical surface. Our approach is based on formulating the equations in a skew-symmetric form, and then discretizing the resultant equations based on the Legendre method. The stability of the scheme can be established at the semi-discrete level. In addition, the scheme preserves mass conservation. The performance of the scheme is validated through several numerical examples, and the performance is as expected.</p>

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An Entropy Stable Pseudospectral Scheme for Shallow Water Equations in Skew-Symmetric Form on a Cubed Sphere

  • 期刊论文

  • 发表日期：

    2025年5月16日

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  • Ting-An Chen,
  • Chun-Hao Teng

摘要

In this study we present a pseudospectral scheme for solving shallow water equations on a spherical surface. Our approach is based on formulating the equations in a skew-symmetric form, and then discretizing the resultant equations based on the Legendre method. The stability of the scheme can be established at the semi-discrete level. In addition, the scheme preserves mass conservation. The performance of the scheme is validated through several numerical examples, and the performance is as expected.