Ghost Fluid Method for Strong Shock Interactions Part 2: Immersed Solid Boundaries

Abstract

Numerical simulation of shock waves interacting with multimaterial interface is immensely challenging, particularly when the embedded interface is retained as a sharp entity. The challenge lies in accurately capturing and representing the interface dynamics and the wave patterns at the interface. In this regard, the ghost fluid method has been successfully used to capture the interface conditions for both fluid-fluid and solid-fluid interfaces. However, the ghost fluid method results in over/underheating errors when shocks impact interfaces, and hence must be supplemented with numerical corrective measures to mitigate these errors. Such corrections typically fail for strong shock applications. Variants and extensions ofthe ghost fluid method have been proposed to remedy its shortcomings with mixed success. In this paper, the performance of approaches based on the ghost fluid method, in the case of strong shocks impinging on immersed solid boundaries in compressible flows, is evaluated. It is found that (from the viewpoint of simplicity, robustness, and accuracy) a reflective boundary condition used in conjunction with a local Riemann solver at the interface proves to be a good choice. The method is found to be stable, accurate, and robust for wide range problems involving strong shocks interacting with embedded solid objects.