Investigation Of Front Tracking Method For Multi-component Flow And Error Analysis

In computational fluid dynamics, the numerical simulation of compressible multi component flow is an extremely urgent and challenging task. In recent years, the study of this problem has been developed rapidly. Since the front tracking method can accurately capture the interface, it has attracted much attention. However, the implementation of front tracking method is relatively complex. The main object of this thesis is to study the key technology of front tracking method based on the Riemann problem. Besides, some discussions about the error of calculation are made and several efficient front tracking methods are developed to simulate compressible multi component flow.The content of thesis has the following parts:1. Study about the shock limiter of front tracking method.First, two shock limiters are constructed for gas-gas and gas-water interface problems. The parameter is determined based on the average conservative error, 1L error and shock strength. Then a universal shock limiter is given for the general equations of state and used to construct ghost fluid states. The HLLC method without iteration is used for the Riemann problem with general equations of state. According to the switch of shock limiter, the initial conditions of Riemann problem are obtained at the interface. It greatly reduces the numerical error. At the same time, the "overheating" problem in numerical simulation has been effectively overcome.2. The Riemann problem is solved to define the boundary conditions with smaller conservative error. The MGFM and RGFM are mainly studied in this thesis. In addition, a new kind of Ghost Fluid method(SGFM) is developed. RGFM and SGFM are all second order. At the same time, the influence of interface boundary conditions, the numerical scheme and the property of material on the average conservative error and 1L error is investigated. Based on the numerical results, the following conclusions can be achieved. First, the definition of density at the interface can affect the numerical results; Second, the MGFM method has larger conservative error than other two methods at the initial time; Third, the RGFM method can consistently make smaller 1L error when employing MUSCL scheme or WENO scheme to simulate the gas-gas interface problems with high pressure and density gas. While the MGFM method performs well in the application of solving the other gas-gas and gas-water interface problems. Fourth, it is necessary for gas water interface problems to use high order method.3. The Riemann problem is constructed in the normal direction of interface. A front tracking method is developed for two-dimensional compressible multi fluid flow. This method includes the following processes: determine the ghost fluid state, calculate the flow field, update and reconstruct the interface. The applicability of MGFM and RGFM is investigated. Numerical results show that the proposed method is efficient.4. A conservative front tracking method is developed for one-dimensional compressible multi fluid flow. The flux is determined by using the solution of Riemann problem at the interface. A high order finite volume scheme is used for the whole flow field. Then conservative variables are redistributed through the conservative interpolation in the new grid so that the method is conservative. Compared with the non conservative front tracking method, the conservative front tracking method can more accurately calculate the shock position as well as the wave state.