The accuracy of the modified ghost fluid method for gas–gas Riemann problem

Previous numerical tests have shown that the modified ghost fluid method (MGFM) [T.G. Liu, B.C. Khoo, K.S. Yeo, Ghost fluid method for strong shock impacting on material interface, J. Comput. Phys. 190 (2003) 651–681; T.G. Liu, B.C. Khoo, C.W. Wang, The ghost fluid method for compressible gas–water simulation, J. Comput. Phys. 204 (2005) 193–221] is robust and performs much better than the original GFM [R.P. Fedkiw, T. Aslam, B. Merriman, S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys. 152 (1999) 457–492]. In this work, a rigorous analysis is carried out on the accuracy of the MGFM when applied to the gas–gas Riemann problem. It is shown that at the material interface the MGFM solution approximates the exact solution to at least second-order accuracy in the sense of comparing to the exact solution of a Riemann problem. On the other hand, the results by the original GFM have generally no-order accuracy if the interface is not in normal motion.