A Conservative Sharp-Interface Numerical Method for Two-dimensional Compressible Two-phase Flows

In this work, a conservative sharp-interface numerical method is developed to simulate compressible two-medium flows with a free interface. In the method, the cut-cell method is introduced to achieve a sharp interface. To avoid the complicated geometric cell merging approach in the cut-cell method, the small cut cells are updated using a flux/conserved variable merging/mixing method that considers the type of small cut cells (general, singular, and vanished). In addition, the residual conserved quantity is redistributed to ensure conservation during the re-initialization process of the level set function. Moreover, to handle thin or small-scale structures where the numerical oscillation may appear, the mixing cut-cell and ghost fluid method is adopted to update these cut cells with a conserved variables mixing approach. Various numerical tests are performed to verify the conservation and robustness of the proposed method.