Development of an Immersed Boundary Method for High-Speed Compressible Flows

Immersed Boundary Methods (IBM) allow modeling fluid-solid interactions via structured grids. Thus, meshing can be avoided and highly efficient structured grid flow solvers can be utilized. In the current study, we utilize a Ghost Cell Method that relies on interpolation for determining approximate boundary conditions in the ghost cells. However, for high-speed compressible flow regimes, discontinuities in the flow can affect the interpolation accuracy and compromise the solution accuracy and stability. This issue is known to affect high-order interpolations, which can provide superior accuracy for continuous flows. Non-linear interpolation techniques can allow high-order interpolation that is oscillation free. This work introduces an implementation, verification, and validation of a standard low-order interpolation IBM technique in our massively parallel compressible flow solver - Athena-RFX++. Then, for the first time, a new approach for high-order non-linear interpolation based on the Fake Nodes Method is coupled with the IBM. The performance of the Fake Nodes Method is extensively compared against typical low- and high-order interpolation techniques.