A high-order no image point sharp interface immersed boundary method for compressible flows

Abstract

A high-order no-image point sharp interface immersed boundary method for compressible flow is presented. The method comprises a stable high-order compact scheme and a ghost point value determination method. By regulating dissipation, the stability of the compact scheme for either Dirichlet or Neumann boundary conditions is validated by the von Neumann method in one dimension. With regard to the use of ghost points, mirror points or Lagrange points are no longer employed. The boundary conditions at the intersection of arbitrary geometries and Cartesian grids are imposed on the basis function of Taylor polynomial interpolation, along with weighted least squares error minimization, in order to determine the values of the ghost points. Third-order accuracy is maintained for both subsonic and supersonic inviscid flow. Numerical simulations of several two-dimensional benchmark problems are carried out to provide evidence about the convergence order of the method.