论文标题
二阶有限体积方案的浅水方程
Second Order Finite Volume Scheme for Shallow Water Equations on Manifolds
论文作者
论文摘要
在这项工作中，我们为一般的协变量坐标提出了一个二阶准确方案。特别是，与歧管相关的度量张量诱导了一般协变量坐标中的协变量参数化。然后，该模型以双曲线形式重新编写，并带有一个元组的保守变量，既组成了不断发展的物理量和度量系数。该公式允许数值方案i）自动计算歧管的曲率，只要物理变量进化并ii）II）在简单的计算域上使用数值研究复杂的物理域。
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.
