An Adaptive Moving Mesh Method for the Five-Equation Model

The five-equation model of multi-component flows has been attracting much attention among researchers during the past twenty years for its potential in the study of the multi-component flows. In this paper, we employ a second order finite vol-ume method with minmod limiter in spatial discretization, which preserves local ex-trema of certain physical quantities and is thus capable of simulating challenging test problems without introducing non-physical oscillations. Moreover, to improve the numerical resolution of the solutions, the adaptive moving mesh strategy proposed in [Huazhong Tang, Tao Tang, Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws, SINUM, 41: 487-515, 2003] is applied. Furthermore, the proposed method can be proved to be capable of preserving the velocity and pres-sure when they are initially constant, which is essential in material interface capturing. Finally, several classical numerical examples demonstrate the effectiveness and robust-ness of the proposed method.