A Cartesian Compact Scheme for the Navier-Stokes Equations in Streamfunction Formulation in Irregular Domains

摘要

In Ben-Artzi et al. (SIAM J Numer Anal 47:3087-3108, 2009) we introduced an embedded Cartesian scheme for the biharmonic problem in two dimensions. Here we extend this methodology to the 2D Navier-Stokes system. Hermite (or Birkhoff) interpolation is invoked in one and two dimensions to obtain finite difference operators. The consistency analysis of the discrete formulas for irregular grids is emphasized. Numerical results demonstrate remarkable accuracy for a series of test cases for flows in elliptical domains.