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 highorder 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.