Extending the Kurganov Riemann-free solver to compressible multi-fluid flows with a sharpening consistent algorithm

There are plenty of examples of compressible multi-fluid flows in the fields of aerospace and defense engineering, the accurate computation and prediction of which are of great significance. Compared to single-fluid flows, compressible multi-fluid flows involve complex phenomena such as shock waves, interfaces, and nonlinear equations of state, which pose considerable numerical challenges. In this study, the Kurganov Riemann-free solver is extended to the γ-based compressible multi-fluid formulation with a newly consistent algorithm. This algorithm satisfies both the single material consistency criterion and the pure material interface criterion. Furthermore, incorporating the boundary variation diminishing (BVD) method, a high-resolution compressible multi-fluid flow solver with interface-sharpening capability is developed. The proposed solver accurately captures both shock waves and interfaces, with interface thickness consistently compressed to approximately 3 computational cells. Several shock-bubble interaction problems were then well reproduced, demonstrating the new solver’s ability to preserve sharp interface features and capture small-scale vortical structures generated during the interaction between shock wave and complex interface with high-density ratio.