In this work, we propose a second-order accurate scheme for shallow water equations in general covariant coordinates over manifolds. In particular, the covariant parametrization in general covariant coordinates is induced by the metric tensor associated to the manifold. The model is then re-written in a hyperbolic form with a tuple of conserved variables composed both of the evolving physical quantities and the metric coefficients. This formulation allows the numerical scheme to i) automatically compute the curvature of the manifold as long as the physical variables are evolved and ii) numerically study complex physical domains over simple computational domains.

翻译：在这项工作中,我们提议了一种二阶精确的浅水方程方案,其一般共变式坐标为多元体。特别是,一般共变式坐标的共变式对等法由与多元体相关的公分数分数引出。然后,该模型以双曲形式重新写成,其中含有由变化中的物理数量和公分数组成的一系列节能变量。这一公式允许数字公式(i) 只要物理变量演变,就自动计算多元体的曲线;以及(ii) 以数字方式对简单的计算域进行复杂的物理域研究。