A diffuse-interface immersed boundary method for simulation of compressible viscous flows with stationary and moving boundaries

In this paper, a diffuse-interface immersed boundary method (IBM) is proposed for simulation of compressible viscous flows with stationary and moving boundaries. In the method, the solution of flow field and the implementation of boundary conditions are decoupled into two steps by applying the fractional step technique, ie, the predictor step and the corrector step. Firstly, in the predictor step, the intermediate flow field is resolved by a recently developed gas kinetic flux solver (GKFS) without consideration of the solid boundary. The GKFS is a finite volume approach that solves the Navier-Stokes equations for the flow variables at cell centers. In GKFS, the inviscid and viscous fluxes are evaluated as a single entity by reconstructing the local solution of continuous Boltzmann equation. Secondly, in the corrector step, the intermediate flow field is corrected by the present diffuse-interface IBM. During this process, the velocity field is firstly corrected by the implicit boundary condition–enforced IBM so that the no-slip boundary condition can be accurately satisfied. After that, the density correction is made by an iterative approach with the help of the continuity equation. Finally, the correction of the temperature field is made in the same way as that of the velocity field. Good agreements between the present simulations and the reference data in literature demonstrate the reliability of the proposed method.