Abstract
An immersed boundary method for simulating compressible viscous flows is presented. The boundary conditions on the immersed boundaries are imposed by a ghost point treatment. The immersed boundaries are represented as a sharp interface. An adaptive selection technique of interpolating polynomials is used to evaluate the values at the ghost points. The present approach effectively avoids numerical instabilities caused by matrix inversion and leads to a robust means of interpolation in the vicinity of the boundaries. The immersed boundary method is implemented in a finite-difference solver for the direct numerical simulation of the compressible Navier-Stokes equations on non-staggered Cartesian grids. The accuracy and fidelity of the solver are examined by the three-dimensional numerical simulation of the thermal convection in a rotating spherical shell. The numerical results are compared with a well-resolved simulation on the spherical coordinate grids.
