论文标题
高阶渐近降级保存均衡的有限差差异方案，用于重力
High order asymptotic preserving well-balanced finite difference WENO schemes for all Mach full Euler equations with gravity
论文作者
论文摘要
在本文中，我们为所有具有重力源项的MACH EULER方程提供了高级半平均有限差异方案。为了获得渐近保存特性，我们从全面可压缩欧拉方程的保守形式开始，并添加电势温度扰动的演化方程。然后将所得的系统分成（非Stiff）非线性低动态材料波，以明确处理，并（僵硬）快速的声学和重力波被隐式处理。借助于潜在温度扰动的显式时间演变，我们为保守变量设计了一种新型的有限差异差异方案，这可以证明是渐近地保存和渐近的不可压缩极限。提供了广泛的数值实验来验证这些特性。
In this paper, we propose a high order semi-implicit well-balanced finite difference scheme for all Mach Euler equations with a gravitational source term. To obtain the asymptotic preserving property, we start from the conservative form of full compressible Euler equations and add the evolution equation of the perturbation of potential temperature. The resulting system is then split into a (non-stiff) nonlinear low dynamic material wave to be treated explicitly, and (stiff) fast acoustic and gravity waves to be treated implicitly. With the aid of explicit time evolution for the perturbation of potential temperature, we design a novel well-balanced finite difference WENO scheme for the conservative variables, which can be proven to be both asymptotic preserving and asymptotically accurate in the incompressible limit. Extensive numerical experiments were provided to validate these properties.
