Front Tracking Method Based On The Riemann Problem

The front-tracking method is applied to the two-dimensional compressible multi-material flow,mainly including numerical solution for the control equation, the determination of the new interfaceand the definition of boundary conditions on the interface based in this thesis. As the normal velocityof interface is defined by the solutions of Riemann problems which are constructed on the interface, amore accurate location of the interface is obtained. The modified Ghost Fluid method (MGFM) andthe real Ghost Fluid Method (RGFM) are proved to be practical and compared in application throughthe numerical simulation results of gas-gas and gas-water interface problems in one-dimension. AndRGFM is determined to be used in two-dimensional problems. The Riemann problems are also solvedto define the boundary conditions for fluid with the ghost-fluid method used to define the conditionsof ghost points on both sides of the interface, respectively.Euler equation is used as the governing equation in this thesis. In order to solve themulti-dimensional Euler equations, dimensional splitting method is applied. An approximate Riemannsolver, which called HLLC scheme, is used to get face flux and optimal second TVD Runge-Kuttamethod to time discretization. We constructed a MUSCL scheme related to five grids using aMINMOD slope limiter to inhibit non physical shocks near the interface.Finally, two R-T problems, shock wave hitting bubbles and SOD tube are simulated as examples,which prove the effectiveness and feasibility of the GFM-FT method for two-dimensionalcompressible multi-fluid flow numerical simulation.