Modified Ghost Fluid Method with Axisymmetric Source Correction (MGFM/ASC)

In this work, we show that the modified ghost fluid method might suffer pressure mismatch at material interfaces and thus leads to inaccurate numerical results when directly applied to long term simulations of multi-medium flow problems with an axisymmetric source term. We disclose the underlying reason and then develop a technique of linear distribution to take into account the effect of the axisymmetric source on the definition of ghost fluid states. In order to faithfully consider the effect of the source term, the interfacial conditions related to derivatives are derived and linear distributions of ghost fluid states are constructed based on a generalized axisymmetric multi-medium Riemann problem. Theoretical analysis and numerical results show that the modified ghost fluid method with axisymmetric source correction (MGFM/ASC) can effectively eliminate the pressure error.