A SECOND-ORDER MODIFIED GHOST FLUID METHOD (2ND-MGFM) FOR 2D PLANAR AND AXISYMMETRIC COMPRESSIBLE MULTIMEDIUM FLOWS*

In this work, we develop a second-order modified ghost fluid method (2nd-MGFM) to simulate two-dimensional (2D) planar and axisymmetric compressible multimedium flow with an immiscible interface. To treat the material interface with higher-order accuracy, we develop the balanced conditions related to spatial derivatives at material interfaces for 2D planar and axisymmetric compressible multimedium flows. We then employ these balanced conditions to describe the interfacial physical properties and disclose that these conditions cannot be satisfied for the current ghost fluid methods, resulting in a first-order temporal error occurring in the region of the interface. To fix this difficulty, a multimedium generalized Riemann problem is proposed to predict the states and the spatial derivatives along the normal direction at the interface, in which the balanced conditions are imposed. Theoretical analysis and numerical results show that the proposed 2nd-MGFM can satisfy these balanced conditions, effectively eliminate the first-order major error term, suppress numerical overheating, and improve mass conservation.