A Conservative Sharp Interface Method for Compressible Two-Medium Flows on Unstructured Triangular Meshes (Advances in Applied Mathematics and Mechanics, 2025)
A conservative sharp interface method based on the cut-cell approach is proposed for the simulation of compressible two-medium flows on unstructured triangular meshes. In this method, the governing equations for each medium are solved using a MUSCL-type finite volume scheme. The exact two-medium Riemann problem is solved at the moving interface, while the local Lax–Friedrichs flux is employed along the fixed cell edges. The interface is tracked by solving the advection equation for the level set function, and explicit interface reconstruction is performed at each time step within the cut-cell framework. To address the small cell problem and ensure global conservation, a novel cell-merging algorithm, specifically designed for unstructured triangular meshes, is introduced to ensure that interface cells coincide with the interface. In contrast to existing cut-cell methods used on Cartesian meshes, the complexity of the new algorithm in constructing cut cells is significantly reduced. Additionally, the adaptive mesh refinement technology is employed to efficiently simulate complex flow problems while reducing the computational cost. A series of numerical tests is conducted to demonstrate the conservativeness and accuracy of the proposed method.