A γ -based compressible multiphase model with cavitation based on discontinuous Galerkin method

The treatment of material interface and cavitation in compressible flow brings difficulties and challenges for numerical simulation, which is also a research field of great significance. Therefore, we present a discontinuous Galerkin (DG) method to simulate cavitation in multiphase flow by combining the γ-based model and a cutoff cavitation model. The DG scheme is adopted for the spatial discretization on an unstructured mesh, and the positivity-preserving limiter is extended to the γ-based model to ensure the parabolicity of the system. Then the eigenvectors of the Jacobian matrices obtained by replacing the total energy in the conservative variables with the pressure are provided for the weighted essentially non-oscillatory reconstruction. In addition, the cutoff model is introduced to suppress the non-physical negative pressure and maintain the accuracy of the peak pressure at the boundary of cavitation. Finally, some numerical results also verify the feasibility of the simple scheme proposed to deal with the cavitation problems and show high accuracy and robustness.