A LEVEL SET METHOD FOR TRACKING INTERFACES IN UNSTEADY COMPRESSIBLE FLOWS

The present work is concerned with the time accurate numerical solution of Euler equationscoupled with the level set method to deal with the topological changes of the interface ofcompressible gas-gas flows. The simulation is conducted by solving the unsteady compressibleEuler equations along with the equation of state for an ideal gas. The scheme is implemented inconjunction with an implicit-unfactored method which is based on Newton-type sub-iterationsand Gauss–Seidel relaxation and matrix preconditioning. The high-order flux reconstruction is anaveraging procedure in which the flow varies. Subsequently, the fluxes are calculated at the cellfaces by a hybrid scheme which is a combination of Riemann method and the modified Stegerand Warming Flux Vector Splitting method. The characteristics values at the cell faces are performed by a modified MUSCL scheme. The performance of the solver has been assessedthrough a series of numerical experiments of interaction of weak shock wave with cylindrical,sinusoidal and inclined interfaces separating two different gases. The numerical image, evolutionof the interface, and growth rate behaviour are seen to agree well with the previous experimentaland numerical results.