An efficient Ghost Fluid Method to remove overheating from material interfaces in compressible multi-medium flows

Abstract

The Ghost Fluid Method (GFM) and its derivatives represent powerful techniques in the numerical simulation of compressible, multi-medium flows, but are nonetheless afflicted by so-called overheating errors at and near material interfaces. These errors take the form of local overshoots and undershoots, and cause the numerical solution to deviate from the exact solution. Overheating errors are commonly addressed by an isobaric fix (or an isentropic fix), where the values at the cells next to the fluid interface are corrected to reduce the numerical diffusion stemming from overheating. These approaches however, do not completely remove overheating, and numerical inaccuracies persist near the interface. In this article, we propose a new version of the GFM called the Efficient Ghost Fluid Method (EGFM) capable of completely eliminating overheating errors, leading to highly accurate solutions near the interface. The EGFM approach has been implemented in IMPACT, a multi-medium, shock physics code, and has been validated against a wide range of 1D and 2D test cases, including problems with surface tension. These include single- as well as multi-medium shock tube problems, various shock-interface interactions, and shock-driven instabilities.