不连续性分类
无粘流
数学
数学分析
边界(拓扑)
间断(语言学)
系数矩阵
边值问题
泊松方程
变量(数学)
欧拉方程
应用数学
机械
物理
特征向量
量子力学
作者
Xudong Li,Ronald Fedkiw,Myungjoo Kang
标识
DOI:10.1006/jcph.2000.6444
摘要
Interfaces have a variety of boundary conditions (or jump conditions) that need to be enforced. The Ghost Fluid Method (GFM) was developed to capture the boundary conditions at a contact discontinuity in the inviscid Euler equations and has been extended to treat more general discontinuities such as shocks, detonations, and deflagrations and compressible viscous flows. In this paper, a similar boundary condition capturing approach is used to develop a new numerical method for the variable coefficient Poisson equation in the presence of interfaces where both the variable coefficients and the solution itself may be discontinuous. This new method is robust and easy to implement even in three spatial dimensions. Furthermore, the coefficient matrix of the associated linear system is the standard symmetric matrix for the variable coefficient Poisson equation in the absence of interfaces allowing for straightforward application of standard “black box” solvers.
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