A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An add...A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features of the model are that it is hyperbolic with only three wave propagation speeds and the volume fraction remains positive. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Moreover, a pressure relaxation procedure is used to fulfill the interface conditions. For validation, the results of suggested scheme are compared with those from the high resolution central upwind and HLLC schemes. The central upwind scheme is also applied for the first time to this model. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential for modeling two-phase flows.展开更多
In this paper,we study a kind of 2-dimensional axi-symmetrical piston problem in com- pressible flow.The corresponding mathematical model is the well-known Euler system.With the Newton iteration procedure and energy e...In this paper,we study a kind of 2-dimensional axi-symmetrical piston problem in com- pressible flow.The corresponding mathematical model is the well-known Euler system.With the Newton iteration procedure and energy estimate,we give the local existence of the shock front solution to this problem.展开更多
文摘A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features of the model are that it is hyperbolic with only three wave propagation speeds and the volume fraction remains positive. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Moreover, a pressure relaxation procedure is used to fulfill the interface conditions. For validation, the results of suggested scheme are compared with those from the high resolution central upwind and HLLC schemes. The central upwind scheme is also applied for the first time to this model. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential for modeling two-phase flows.
基金Supported partially by NSFC Project 10131050 and NSFC Project 10271108
文摘In this paper,we study a kind of 2-dimensional axi-symmetrical piston problem in com- pressible flow.The corresponding mathematical model is the well-known Euler system.With the Newton iteration procedure and energy estimate,we give the local existence of the shock front solution to this problem.
基金Supported by the National Natural Science Foundation of China(11371248)the Natural Science Foundation of the Education Department of Anhui Province,China(KJ2015A347)the Key Projects of Outstanding Young Talents of Universities in Anhui Province(gxyq ZD2016520)
