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In the present Paper, solution methods for simulating compressible flows and shock wave simulation by using Lattice Boltzmann Method(LBM) and simulation of shock wave in the bubble with a moving boundary is evaluated. The standard LBM is found to be incapable of predicting compressible flows and confront instabilities in high Mach number flows. But with some efforts that has been made in recent years, new models for stable solutions of the compressible equations are established. Modified Lax–Wendroff finite difference scheme that has stabale solutions has been used for discretizing Lattice Boltzmann equation. In this study models based on the compressible Euler and compressible multispeed Navier-Stokes to simulate compressible lattice Boltzmann method have been used. The dynamics of compressible bubble busing Rayleigh-Plesset equation have been obtained. Simulation of shock wave in the bubble with other computational fluid dynamics methods has been carried out, However, due to the weakness of the Lattice Boltzmann method for compressible flow, no effort to study the physic of this phenomena has been done with this method. The purpose of this simulation is to achieve a distribution of thermodynamic properties through the radius while collapsing and eventually forming the Sonoluminescence phenomena that caused by the collision of shock waves in the center of the bubble to one other,with lattice boltzmann method.

Keywords: Compressible flow, Shock Wave, Lattice Boltzmann, Modified Lax-wendroff, Rayleigh Plesset

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