On the Dynamics of Shock-Interface Interaction using the Level Set Method

A.  Bagabir; A.  Balabel; W. A.  El-Askary

Authors

A. Bagabir Faculty of Engineering, Sana’a University, P. O. Box 13282, Sana’a, Yemen
A. Balabel Faculty of Engineering, Menofia University Shebin Elkom, Menofia, Egypt
W. A. El-Askary Faculty of Engineering, Menofia University Shebin Elkom, Menofia, Egypt

Keywords:

shock-interface interaction, shock-bubble interaction, level-set method, gas-gas interface, two- dimensional flow, euler equations, unsteady compressible flow

Abstract

The present work is concerned with the time accurate numerical solution of Euler equations coupled with the level set method to deal with the topological changes of the interface in compressible gas-gas flows due to an incident shock. The simulation is conducted by solving the unsteady compressible Euler equations along with the equation of state for an ideal gas. The scheme is implemented in conjunction with an implicit-unfactored method which is based on Newton-type sub-iterations and Gauss–Seidel relaxation and matrix preconditioning. The high-order flux reconstruction is an averaging procedure in which the flow variables and, subsequently the fluxes, are calculated at the cell faces by hybrid scheme. It is a combination of Riemann method and the modified Steger and Warming Flux Vector Splitting (FVS) method. The characteristics values at the cell faces are performed by a modified MUSCL scheme. The performance of the solver has been assessed through a series of numerical experiments of interaction of weak shock wave with cylindrical, sinusoidal and inclined interfaces separating two different gases. The present results, including numerical image, evolution of the interface, and growth rate behaviour, are seen to be in agreement with the available previous numerical and experimental data.