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

This note gives a numerical investigation for the popular high resolution conservativeschemes when applied to inviscid, compressible, perfect gas °ows with an initial highdensity ratio as well as a high pressure ratio. The results show that they work veryine±ciently and may give inaccurate numerical results even over a very ?ne meshwhen applied to such a problem. Numerical tests show that increasing the order ofaccuracy of the numerical schemes does not help much in improving the numericalresults. How to cure this di±culty is still open.

We propose a methodology based on the boundary element method (BEM) to simulate pressure pulse–bubble interaction. The pulseresembles a shock wave and is in the form of a step pulse function incorporated into the Bernoulli equation. Compressibility effects of thewater surrounding the bubble are neglected, and the dynamic response of the bubble to the impinging pulse is assumed to be mainlyinertia controlled. The interaction induces the formation of a high-speed jet that penetrates the bubble. Results show that bubble shape,collapse time and jet velocity are in good agreement with other numerical models and experiments, and the method is more computationallyefficient.

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.

An underwater explosion near a free surface constitutes an explosive gas–water–air system with a shock and free surface interactionand the presence of bulk cavitation region. This paper applies a simplified modified ghost fluid method [T.G. Liu, et al., Comm.Comput. Phys. 1 (2006) 898] to simulate the explosive gas–water and water–air interfaces and an isentropic one-fluid cavitationmodel [T.G. Liu, et al., J. Comput. Phys. 201 (2004) 80] to describe and capture the unsteady cavitation just below the free surface.It is found that the proposed ghost fluid method can accurately simulate the gas–water/water–air compressible flows with the waveinteraction at the interfaces and the deformation of the free surface. The isentropic one-fluid cavitation model, on the other hand,is capable of simulating the dynamic creation and evolution of the bulk cavitation below the free surface.