The modified ghost fluid method(MGFM)has been shown to be robust and efficient when being applied to multi-medium compressible flows.In this paper,we rigorously analyze the optimal error estimation of the MGFM when it is applied to the multi-fluid Riemann problem.By analyzing the properties of the MGFM and the approximate Riemann problem solver(ARPS),we show that the interfacial status provided by the MGFM can achieve“third-order accuracy”in the sense of comparing to the exact solution of the Riemann problem,regardless of the solution type.In addition,our analysis further reveals that the ARPS based on a doubled shock structure in the MGFM is suitable for almost any conditions for predicting the interfacial status,and that the“natural”approach of“third-order accuracy”is practically less useful.Various examples are presented to validate the conclusions made.
In this work,the modified ghost fluid method is developed to deal with 2D compressible fluid interacting with elastic solid in an Euler-Lagrange coupled system.In applying the modified Ghost Fluid Method to treat the fluid-elastic solid coupling,the Navier equations for elastic solid are cast into a system similar to the Euler equations but in Lagrangian coordinates.Furthermore,to take into account the influence of material deformation and nonlinear wave interaction at the interface,an Euler-Lagrange Riemann problem is constructed and solved approximately along the normal direction of the interface to predict the interfacial status and then define the ghost fluid and ghost solid states.Numerical tests are presented to verify the resultant method.
