A boundary condition capturing method for Poisson's equation on irregular domains

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 eq uations 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 deve lop a new numerical method for the variable coefficient Poisson equation in the presence of interfaces where both the variable coefficients and the so lution itself may be discontinuous. This new method is robust and easy to i mplement even in three spatial dimensions. Furthermore, the coefficient mat rix of the associated linear system is the standard symmetric matrix for th e variable coefficient Poisson equation in the absence of interfaces allowi ng for straightforward application of standard "black box" solvers. (C) 200 0 Academic Press.