论文标题
针对切细胞网的有限体积方案的状态重新分布算法
A state redistribution algorithm for finite volume schemes on cut cell meshes
论文作者
论文摘要
在本文中，我们开发了一种称为\ textit {state Repistribution}的新技术，该技术允许在将解决方案近似于嵌入的边界网格上的双曲线保护法时使用显式时间步进。状态重新分布是一种在基本有限体积方案的每个时间步长或阶段之后应用的后处理技术，使用与完整单元的体积成正比的时间步。这个想法是通过暂时将其合并到更大的，可能重叠的社区来稳定切割细胞，然后用保持保护和准确性的稳定值代替切割单元的值。我们使用两个基本方案介绍了状态重新分布的示例：MUSCL和线条有限体积方案的二阶方法。状态重新分布用于计算切割细胞网的气体动力学的几种标准测试问题，并具有光滑和不连续的溶液。我们表明，我们的方法不会降低基本方案的准确性，并且以非振荡方式成功捕获冲击。
In this paper we develop a new technique, called \textit{state redistribution}, that allows the use of explicit time stepping when approximating solutions to hyperbolic conservation laws on embedded boundary grids. State redistribution is a postprocessing technique applied after each time step or stage of the base finite volume scheme, using a time step that is proportional to the volume of the full cells. The idea is to stabilize the cut cells by temporarily merging them into larger, possibly overlapping neighborhoods, then replacing the cut cell values with a stabilized value that maintains conservation and accuracy. We present examples of state redistribution using two base schemes: MUSCL and a second order Method of Lines finite volume scheme. State redistribution is used to compute solutions to several standard test problems in gas dynamics on cut cell meshes, with both smooth and discontinuous solutions. We show that our method does not reduce the accuracy of the base scheme and that it successfully captures shocks in a non-oscillatory manner.
