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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 boundary condition of the stream function. Numerical examples that show second order accuracy of the computed solution are also provided.

A Fast Finite Differenc Method For Solving Navier-Stokes Equations on Irregular Domains