论文标题
高阶离散均衡的方法是任意静水气氛的
High order discretely well-balanced methods for arbitrary hydrostatic atmospheres
论文作者
论文摘要
我们介绍了带有重力源项的完整可压缩欧拉系统的新型高阶均衡有限体积方法。他们不需要对静水溶液的先验知识，该溶液必须具有良好的平衡，并且不仅限于某些类别的静液压溶液。在一个空间维度中，我们构建了一种准确平衡任何静液压状态的高阶离散化的方法。该方法使用每个单元格中静水态的局部高阶近似延伸到两个空间维度。提出的简单，灵活和鲁棒的方法不仅限于特定状态方程。数值测试验证了所提出的方法是否提高了准确解决静液压状态的小扰动的能力。
We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not restricted to certain classes of hydrostatic solutions. In one spatial dimension we construct a method that exactly balances a high order discretization of any hydrostatic state. The method is extended to two spatial dimensions using a local high order approximation of a hydrostatic state in each cell. The proposed simple, flexible, and robust methods are not restricted to a specific equation of state. Numerical tests verify that the proposed method improves the capability to accurately resolve small perturbations on hydrostatic states.
