Unconditionally Stable Convergent Finite Difference Method for Navier-Stokes Problems on Curved Domains

摘要

A new finite difference scheme is presented for solving two dimensional, transient, imcompressible, Navier Stokes problems on a bounded simply connected region for which there exists a C-2 invertible mapping onto the unit square. The method is proven to be unconditionally stable and convergent, and reduces to the well-known Krzhivitsky and Ladyzhenskaya scheme for rectangular domains.