An adaptive ghost uidnite volume method is developed for one{ and two dimensional compressible multi-medium ows in this work. It couples the real ghostuid method (GFM) [SIAM J. Sci. Comput. 28 (2006) 278] and the adaptive moving mesh method [SIAM]. Numer. Anal. 41 (2003) 487; J. Comput. Phys. 188 (2003) 543], and thus retains their advantages. This work shows that the local mesh clus-tering in the vicinity of the material interface can efiectively reduce both numerical and conservative errors caused by the GFM around the material interface and other discontinuities. Besides the improvement of oweld resolution, the adaptive ghost uid method also largely increases the computational eciency. Several numerical experiments are conducted to demonstrate robustness and e±ciency of the current method. They include several 1D and 2D gas-water problems, involving a large density gradient at the material interface and strong shock-interface interactions. The results show that our algorithm can capture the shock waves and the material interface accurately, and is stable and robust even solution with large density and pressure gradients

The original ghost fluid method (GFM) developed in [13] and the modifiedGFM (MGFM) in [26] have provided a simple and yet flexible way to treat twomediumflow problems. The original GFM and MGFM make the material interface "invisible" during computations and the calculations are carried out as for a singlemedium such that its extension to multi-dimensions becomes fairly straightforward.The Runge-Kutta discontinuous Galerkin (RKDG) method for solving hyperbolic conservationlaws is a high order accurate finite element method employing the usefulfeatures from high resolution finite volume schemes, such as the exact or approximateRiemann solvers, TVD Runge-Kutta time discretizations, and limiters. In this paper,we investigate using RKDG finite element methods for two-medium flow simulationsin one and two dimensions in which the moving material interfaces is treated via nonconservativemethods based on the original GFM and MGFM. Numerical results forboth gas-gas and gas-water flows are provided to show the characteristic behaviors ofthese combinations.

The dynamic response of deformable structures subjected to shock load and cavitation reload has been simulated using a multiphase model, which consists of an interface capturing method and a one-fluid cavitation model. Fluid-structure interaction (FSI) is captured via a modified ghost fluid method (Liu et al. in J Comput Phys 190: 651-681, 2003), where the structure is assumed to be a hydro-elasto-plastic material if subjected to a strong shock load. Bulk cavitation near the structural surface is captured using an isentropic model (Liu et al. in J Comput Phys 201:80–108, 2004). The integrated multiphase model is validated by comparing numerical predictions with 1D analytical solutions, and with numerical solutions calculated using the cavitation acoustic finite element (CAF?) method (Sprague and Geers in Shocks vib 7: 105-122, 2001). To assess the ability of the multiphase model for multi-dimensions, underwater explosions (UNDEX) near structures are computed. The importance of cavitation reloading and FSI is investigated. Comparisons of the predicted pressure time histories with different explosion center are shown, and the effect on the structure is discussed.

Previous numerical tests have shown that the modified ghost fluid method (MGFM) [T.G. Liu, B.C. Khoo, K.S. Yeo, Ghost fluidmethod 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 muchbetter than the original GFM [R.P. Fedkiw, T. Aslam, B. Merriman, S. Osher, A non-oscillatory Eulerian approach to interfaces inmultimaterial flows (the ghost fluid method), J. Comput. Phys. 152 (1999) 457-492]. In this work, a rigorous analysis is carriedout on the accuracy of the MGFM when applied to the gas-gas Riemann problem. It is shown that at the material interface theMGFM solution approximates the exact solution to at least second-order accuracy in the sense of comparing to the exact solutionof a Riemann problem. On the other hand, the results by the original GFM have generally no-order accuracy if the interface is notin normal motion.

The Runge–Kutta discontinuous Galerkin (RKDG) method for solving hyperbolic conservation laws is a high orderfinite element method, which utilizes the useful features from high resolution finite volume schemes, such as the exactor approximate Riemann solvers, TVD Runge–Kutta time discretizations, and limiters. In this paper, we investigate usingthe RKDG finite element method for compressible two-medium flow simulation with conservative treatment of the movingmaterial interfaces. Numerical results for both gas–gas and gas–water flows in one-dimension are provided to demonstratethe characteristic behavior of this approach.