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.
翻译:在本文中,我们提出了一个新颖的第二顺序准确而平衡的浅水方程式方案,它以一般的共变式坐标为方形。在我们的处理方法中,一旦为特定情况确定了引力场,就会通过一个通用共变式坐标框架探测到一个相等的表面,并进行对称。这个表层是其共变对称引致一公吨气压的多元体。然后,模型以双曲形式重新写成一个双曲形,由一个由不断演变的物理数量和公吨系数组成的多维变量组成。这个公式允许数字法在物理变量演变期间自动计算多元的曲度。