论文标题
较浅的水方程的均衡有限体积方案
Well balanced finite volume schemes for shallow water equations on manifolds
论文作者
论文摘要
在本文中，我们提出了一种新型的二阶准确平衡方案，用于一般的协变量坐标，以均高于歧管。在我们的方法中，一旦为特定情况定义了重力场，就会检测到一个等电位的表面并通过一般协变坐标的框架进行参数。该表面是其协变量参数化诱导度量张量的歧管。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自动计算歧管的曲率，只要物理变量进化。
In this paper we propose a novel second-order accurate well balanced scheme for shallow water equations in general covariant coordinates over manifolds. In our approach, once the gravitational field is defined for the specific case, one equipotential surface is detected and parametrized by a frame of general covariant coordinates. This surface is the manifold whose covariant parametrization induces a metric tensor. 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 automatically compute the curvature of the manifold as long as the physical variables are evolved.
