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：本文提出了一种在流形上一般协变坐标系下浅水方程的二阶精确格式。具体而言，由流形相关的度规张量诱导出一般协变坐标系中的协变参数化形式。该模型随后被重写为双曲形式，其守恒变量元组由演化的物理量和度规系数共同构成。此表述允许数值格式：i) 在物理变量演进过程中自动计算流形曲率；ii) 在简单计算域上数值研究复杂物理域。