数学
多边形网格
理论(学习稳定性)
维数(图论)
计算
边界(拓扑)
逆风格式
有限体积法
应用数学
平流
边值问题
数值稳定性
数学分析
数值分析
几何学
算法
计算机科学
纯数学
机械
物理
机器学习
热力学
离散化
标识
DOI:10.1016/j.apnum.2015.05.003
摘要
Embedded boundary meshes may have cut cells of arbitrarily small volume which can lead to stability problems in finite volume computations with explicit time stepping. We show that time step constraints are not as strict as often believed. We prove this in one dimension for linear advection and the first order upwind scheme. Numerical examples in two dimensions demonstrate that this carries over to more complicated situations. This analysis sheds light on the choice of time step when using cell merging to stabilize the arbitrarily small cells that arise in embedded boundary schemes.
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