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A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains (1999)
| Citations: | 105 - 20 self |
BibTeX
@MISC{Liu99aboundary,
author = {Xu-dong Liu and Ronald P. Fedkiw and Myungjoo Kang},
title = {A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains},
year = {1999}
}
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Abstract
Interfaces have a variety of boundary conditions (or jump conditions) that need to be enforced. In [3], the Ghost Fluid Method (GFM) was developed to capture the boundary conditions at a contact discontinuity in the inviscid Euler equations. This method was extended to treat more general discontinuities such as shocks, detonations, and deflagrations in [2] and compressible viscous flows in [4]. 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.
Keyphrases
irregular domain boundary condition capturing method variable coefficient poisson equation boundary condition coefficient matrix contact discontinuity similar boundary condition standard black box solver new method linear system general discontinuity ghost fluid method variable coefficient standard symmetric matrix new numerical method inviscid euler equation straightforward application compressible viscous flow spatial dimension
