A conservative interface treating method for compressible multi-medium flow based on cut-cell method

A conservative sharp interface treating method is proposed based on the cut-cell method. In the compressible multi-medium problems, small-sized cells may occur due to the moving interface and lead to the instability of the algorithm. To overcome this problem, the most common approach is merging the small cells with their neighbors. In this work, we present a new and simple way to construct interface cells without considering various complex cases of cell merging. The interface cells are constructed by connecting cell nodes near the interface along the normal direction of the interface, which can delay the occurrence of small cells efficiently. Meanwhile, the Lagrangian flux at the cell edge moving with the interface is adopted based on the local Riemann problem, thus the conservation of the flow variables is effectively maintained. Several numerical examples are tested to demonstrate the good capability of this proposed method, even for problems with large density and pressure gradients at the interface.