A fast finite difference method is proposed to solve the incompressible Navier-Stokes equations defined on a general domain. The method is based on the vorticity stream-function formulation and a fast Poisson solver defined on a general domain using the immersed interface method. The key to the new method is the fast Poisson solver for general domains and the interpolation scheme for the bounda...

A novel Douglas alternating direction implicit (ADI) method is proposed in this work to solve a two-dimensional (2D) heat equation with interfaces. The ADI scheme is a powerful finite difference method for solving parabolic equations, due to its unconditional stability and high efficiency. However, it suffers from a serious accuracy reduction in space for interface problems with different mater...

Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot’s equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect...