The Level-Set discontinuity tracking technology is extended to the simulation of general compressible multimaterial flows.A Level-Set function is used to keep the track of the interface and discontinuity.A conservative high order accurate WENO scheme is employed.The ghost fluids are constructed in the narrow band region with solution of the Riemann problem.The GFM (ghost fluid method) is implemented for the study of material interface and general discontinuity such as detonation discontinuities.The algorithm is applied to simulate multi-material fluid flows and satisfactory numerical results are obtained.

By predicting the real fluid status rather than the ghost fluid status with a Riemann problem,a simple and efficient extension of the ghost fluid method in multi-dimension is introduced. Riemann problems are constructed at the interface and solved to define boundary conditions of fluid on both sides of the interface.Since the Riemann problem solvers describe fluid state reasonably and the normal velocity and pressure are continuous across the interface,a more accurate interface boundary condition is obtained. Conservation error shows that the method incurs minor errors. Numerical experiments show that this method captures the interface and shock waves correctly.

According to the ENO scheme on structured grids, a class of weighted ENO finite volume scheme on unstructured mesh is developed. On every control volume, it constructs a new weighted quadratic reconstruction polynomial which can save computational costs. It also uses a method which can resolve the overdetermined systems and do not affect the accuracy of the schemes. Besides, the selection of interpolation points and the construction of weight are presented, Third order TVD Runge Kutta time discretization is used. In order to accelerate the convergence, local time step is introduced. The numerical experiments show the scheme effective.