论文标题
用于多物质流的能量拆分高阶数值方法
An energy-splitting high order numerical method for multi-material flows
论文作者
论文摘要
本章基于Baer-Nunziato（BN）模型的一系列简化形式，通过一种有效的数值方法来处理多物质流问题。数值模拟通常面临许多困难的挑战，通常包括多物质冲击的体积分数阳性和稳定性。为了应对这些挑战，我们提出了一种新的非振荡{\ em能量分解} Godunov型方案，用于计算Eulerian框架中的多流体流。引入了一种新颖的BN模型的简化版本，作为能量拆分方案的基础。与通过降低文献中BN模型获得的现有两种物质压缩流模型相比，这表明我们的新还原模型可以非常有效地模拟材料界面周围的动能交换。然后，使用广义的Riemann问题（GRP）求解器制造了能量拆分Godunov型方案的二阶精确扩展。进行了数值实验，以进行冲击接口的相互作用，减震相互作用和Richtmyer-Meshkov不稳定性问题，这证明了这种类型的方案的出色性能。
This chapter deals with multi-material flow problems by a kind of effective numerical methods, based on a series of reduced forms of the Baer-Nunziato (BN) model. Numerical simulations often face a host of difficult challenges, typically including the volume fraction positivity and stability of multi-material shocks. To cope with these challenges, we propose a new non-oscillatory {\em energy-splitting} Godunov-type scheme for computing multi-fluid flows in the Eulerian framework. A novel reduced version of the BN model is introduced as the basis for the energy-splitting scheme. In comparison with existing two-material compressible flow models obtained by reducing the BN model in the literature, it is shown that our new reduced model can simulate the kinetic energy exchange around material interfaces very effectively. Then a second-order accurate extension of the energy-splitting Godunov-type scheme is made using the generalized Riemann problem (GRP) solver. Numerical experiments are carried out for the shock-interface interaction, shock-bubble interaction and the Richtmyer-Meshkov instability problems, which demonstrate the excellent performance of this type of schemes.
