Node-Centered DG Method Coupled with Real-Ghost Fluid Method

A new numerical simulation method was proposed for the complex multi-media interface problem of two-dimensional compressible fluids, which combined the discontinuous Galerkin (DG) method and the real-ghost fluid method (RGFM) to construct a new numerical solver. The solver employed a node-centered DG method for spatial discretization of the Euler equation and a weighted essentially no-oscillation (WENO) reconstruction limiter to suppress unphysical oscillations and to ensure the stability of the numerical format, while the Level-set method and the RGFM were used to accurately capture and process the multimedium interface. In order to verify the effectiveness of this DG-RGFM solver, several numerical examples were computed in this paper, including typical examples of isentropic vortices, the Noh problem, the Sedov problem, the interaction of a strong shock wave in water with an air bubble, and the interaction of a surge wave with a helium bubble. The numerical results show that the proposed DG-RGFM solver is able to effectively simulate complex multimedium interface problems and exhibits good fidelity and robustness, which provides a potentially applicable scheme for the numerical simulation of related problems.