Immersed Boundary Method for Compressible Navier-Stokes Equations

Abstract

For viscous compressible flow, a Cartesian grid approach has been devised to solve the Navier-Stokes equations. Both steady and unsteady fluxes have been taken into account. We treat the nearest grid points as mirror points of the ghost points using a simpler ghost point approach. In the submerged boundary, wall boundary requirements are established at the ghost spots. The method’s accuracy has been examined for a number of test scenarios. We provide numerical instances of supersonic flow in a circular cylinder and comapare them with analytical outcomes. Furthermore, we compute time accurate results of the compressible Navier-Stokes problems for an incidence shock across a cylinder and compare the history with earlier studies. To demonstrate the correctness of the approach, we calculated skin friction profiles and compared the results with the body fitted method. Although it works better, the current approach is based on a simplifed ghost point treatment that was previously established. The results are comparable, although not being as precise as those obtained using more advanced techniques.