一种基于MOF界面重构的二维中心型MMALE方法

发展了一种基于MOF（Moment of Fluid）界面重构的二维中心型MMALE（Multi-Material Arbitrary Lagrangian-Eulerian）方法.其中，流体力学方程组采用中心型拉氏方法进行离散求解.混合网格的热力学封闭采用Tipton压力松弛模型.混合网格内的界面重构采用MOF方法，并对MOF方法作了简化和改进.重映步采用一种基于多边形剪裁算法的精确积分守恒重映方法.计算了若干数值例子，包括二维漩涡发展问题、Sedov问题、激波与氦气泡相互作用问题、水中强激波与空气泡相互作用问题、二维RT不稳定性问题等.数值算例表明，该方法具有二阶精度，能够计算界面两侧密度比和压力比很大的问题，并且其健壮性优于交错型MMALE方法，适合计算多介质复杂流体动力学问题.

A 2 D Cell-centered MMALE Method Based on MOF Interface Reconstruction

A 2D cell-centered multi-material arbitrary Lagrangian-Eulerian(MMALE) method based on moment of fluid(MOF) interface reconstruction is developed. Hydrodynamic equations are discretized and solved by cell-centered Lagrangian scheme. Tipton's pressure relaxation model is adopted as closure model for mixed cells. MOF method is simplified and improved to reconstruct interface in mixed cells. A conservative integral remapping algorithm based on cell-intersection is used in remapping phase. Several numerical examples are given, such as 2D periodic vortex problem, Sedov problem, interaction of a shock wave with an helium bubble,a strong water shock impacting on a cylindrical air bubble in water,2D Rayleigh-Taylor instability, etc.It shows that the method is of second order accurate, and is capable of computing problems involving large density and/or pressure ratios across interface. Its robustness is better than that of staggered MMALE method and it is applicable to complex multi-material hydrodynamic problems.