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. Using analytical solutions, experimental observations, published numerical results, and Galilean transformations, 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. On the basis of the proposed method, the development of a solver that unifies one-, two-, and three-dimensional computations and the generation of complex geometric objects via simply positioning components are described. In addition, a surface-normalized absolute flux is proposed for interface sharpness measurement, and an analytically solvable modified vortex preservation problem is developed for a convergence study concerning smooth flow with irregular geometries.