(untitled) (Communications in Computational Physics, 2023)
The ghost fluid method (GFM) provides a simple way to simulate the interaction of immiscible materials. Especially, the modified GFM (MGFM) and its variants, based on the solutions of multi-material Riemann problems, are capable of faithfully taking into account the effects of nonlinear wave interaction and material property near the interface. Reasonable treatments for ghost fluid states or interface conditions have been shown to be crucial when applied to various interfacial phenomena involving large discontinuity and strong nonlinearity. These methods, therefore, have great potential in engineering applications. In this paper, we review the development of such methods. The methodologies of representative GFM-based algorithms for definition of interface conditions are illustrated and compared to each other. The research progresses in design principle and accuracy analysis are briefly described. Some steps and techniques for multi-dimensional extension are also summarized. In addition, we present some progresses in more challenging scientific problems, including a variety of fluid/solid-fluid/solid interactions with complex physical properties. Of course the challenges faced by researchers in this field are also discussed.