Sharp interface simulations with Local Mesh Refinement for multi-material dynamics in strongly shocked flows

Shock waves interacting with multi-material interfaces in compressible flows result in complex shock diffraction patterns involving total or partial reflection, refraction and transmission of the impinging shock wave. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with levelset interface tracking is attractive. In this regard, a unified Riemann solver based Ghost Fluid Method (GFM) is developed to accurately resolve and represent the embedded solid and fluid object(s) in high speed compressible multiphase flows. In addition, the Riemann solver based GFM approach is augmented with a quadtree (octree in three-dimensions) based Local Mesh Refinement (LMR) technique for efficient and high fidelity computations involving strong shock interactions. The paper reports on a conservative formulation for accurate calculation of ENO-based numerical fluxes at the fine-coarse mesh boundaries. The numerical examples presented in this paper clearly demonstrate that the methodology produces accurate benchmark solutions and effectively captures fine structures in the flow field.