A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
An isobaric fix for the overheating problem in multimaterial compressible flows
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
Computations of compressible multifluids
Journal of Computational Physics
Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method
Journal of Computational Physics
A Real Ghost Fluid Method for the Simulation of Multimedium Compressible Flow
SIAM Journal on Scientific Computing
The accuracy of the modified ghost fluid method for gas--gas Riemann problem
Applied Numerical Mathematics
SIAM Journal on Scientific Computing
A front-tracking/ghost-fluid method for fluid interfaces in compressible flows
Journal of Computational Physics
An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
Since the (original) ghost fluid method (OGFM) was proposed by Fedkiw et al. in 1999 [5], a series of other GFM-based methods such as the gas-water version GFM (GWGFM), the modified GFM (MGFM) and the real GFM (RGFM) have been developed subsequently. Systematic analysis, however, has yet to be carried out for the various GFMs on their accuracies and conservation errors. In this paper, we develop a technique to rigorously analyze the accuracies and conservation errors of these different GFMs when applied to the multi-medium Riemann problem with a general equation of state (EOS). By analyzing and comparing the interfacial state provided by each GFM to the exact one of the original multi-medium Riemann problem, we show that the accuracy of interfacial treatment can achieve ''third-order accuracy'' in the sense of comparing to the exact solution of the original mutli-medium Riemann problem for the MGFM and the RGFM, while it is of at most ''first-order accuracy'' for the OGFM and the GWGFM when the interface approach is actually near in balance. Similar conclusions are also obtained in association with the local conservation errors. A special test method is exploited to validate these theoretical conclusions from the numerical viewpoint.