A Second-order Modified Ghost Fluid Method (2nd-MGFM) with Discontinuous Galerkin Method for 1-D compressible Multi-medium Problem with Cylindrical and Spherical Symmetry

In this work, we develop the discontinuous Galerkin method to simulate 1-D cylindrical and spherical compressible multi-medium flows with an immiscible interface. To treat the interface with higher-order accuracy, the modified ghost fluid method is extended to a second-order version with source terms, in which linearly distributed ghost fluid states are constructed. A multi-medium generalized Riemann problem with the geometrical source is constructed to predict the states and the spatial derivatives at the interface. The predicted interface states and spatial derivatives are then employed to define the linearly distributed ghost fluid states. Theoretical analysis shows that the proposed second-order modified ghost fluid method (2nd-MGFM) can effectively eliminate the first order major error term occurring to the interface and accumulating with time when there is interface acceleration. Numerical results exhibit the proposed 2nd-MGFM can suppress overheating at the accelerating wall and pressure dislocation at the accelerating interface very well.