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In this article, for the first time the numerical solution of Godunov method with HLLC Riemann solver is extended for a hyperbolic five equations two-fluid model. The flow field is considered for two-space dimensional case. So far, two main difficulties include non-monotonic behavior of mixture sound relation and inability of shock transition from interface was mentioned during working with this model. In this research these difficulties were overcome by selecting an appropriate mixture sound relation and appropriate discretization of non-conservative term. The mutual effect of shock wave impact with a droplet and two droplets with different diameters were simulated and studied. During the shock wave impact with 1.47 and 6 Mach with the droplet, a complicated shape of interface was formed with high pressure zone and low pressure zone of cavitations. The results obtained from the present attempt were compared with the experimental and related similar results of that obtained by the other numerical methods and models. The comparison of the results was good. It was also concluded that the numerical method used in the present work has enough accuracy with high capability in capturing two-phase flow interfacial instability and shock wave impact transmission from the droplet.

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This paper presents a new and accurate methodology for transient and dynamic behavior of slug hydrodynamic instability modeling in horizontal and inclined channels. The base of this methodology is on numerical solution of hyperbolic two fluid model equations by means of a class of high resolution shock capturing methods. The privilege of this method is that it can model and predict initiation and growth of slug in stratified flow automatically and directly by solving the flow field differential equations. The well-defined test case considered for the verification and validation of the results is the Ransom Water Faucet case. The results obtained for slug flow modeling in horizontal duct were compared with two sets of experimental results. The good agreement of the present modeling results with the experimental results of own and other investigators and also grid independency study show the model is capable of slug tracking and slug capturing and the numerical method which is used here can predict with high enough accuracy.

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Abstract- The aim of this paper is to develop a numerical procedure for simulating underwater explosion phenomena with a simplified mathematical and two fluid model. The two fluid Kapila five equation model is selected as the governing equations and the ideal gas and Stiffened gas equations of state (SG-EOS) are used to obtain pressure in the gas bubble and the surrounding water zone, respectively. The modified Schmidt EOS is used to simulate the cavitation regions with low pressure. A Godunov numerical method and HLLC Reiman solver is extended for Kapila two fluid model. The numerical results of the present method and comparing them with available experimental results, verify that the proposed method has good capablity of predicting complex physics involved in a spherical underwater explosion and its interaction with free surface. The method also shows a very good performance with no spurious oscillation in cavitation zone simulation in two-dimensional problems

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Numerical modeling of compressible two-phase flow is a challenging and important subject in practical cases and research problems. In these problems, mutual effect of shock wave interaction creates a discontinuity in fluid properties and interface of two fluids as a second discontinuity lead to some difficulties in numerical approximations and estimating an accurate interface during hydro-dynamical capturing process. The objective of this research is to increase the accuracy of numerical simulation of two-phase flow using two dimensional five-equation two-fluid model. For this purposes, MUSCL strategy was used for increasing the Godunov numerical scheme accuracy from 1st order to 2nd order. The privilege of this method is high accuracy, low numerical oscillation and low numerical diffusion. The problems considered for the verification of the results are the water-air shock tube, a square bubble with moving interface in a uniform flow and a shock wave with 1.72 Mach having interaction with an air bubble in a water pool. The obtained numerical results showed that, the results that have been obtained by second order accuracy have less diffusion in the two-phase flow interface.