An immersed boundary method for solving compressible flow with   arbitrarily irregular and moving geometry
  In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy boundary conditions in a straightforward and consistent manner. Equipped with a fluid-solid coupling framework that integrates high-order temporal and spatial discretization schemes, numerical experiments concerning flow involving stationary and moving objects, convex and concave geometries, no-slip and slip wall boundary conditions, as well as subsonic and supersonic motions are conducted to validate the method. It is demonstrated that the proposed method can provide efficient, accurate, and robust boundary treatment for solving flow with arbitrarily irregular and moving geometries on Cartesian grids. 
Huangrui Mo and Fue-Sang Lien and Fan Zhang and Duane S. Cronin
physics.flu-dyn physics.comp-ph