可压缩多介质流动问题的高精度数值模拟方法

High-order numerical simulation method for compressible multi-material flow problems

在可压缩流动问题的数值模拟领域,激波的高分辨率计算已取得重要进展。但是包含物质界面的可压缩多介质流动的数值模拟还存在诸多数值挑战,主要表现为界面处数值耗散过大和非物理振荡等问题。界面处流体性质的不连续性是造成可压缩多介质流动问题物理建模与数值方法困难的主要原因。为了建立一套高效的可压缩多介质流动问题的高精度数值模拟方案,本文从数值框架的选择、非守恒方程相容离散、高精度有界格式构造、界面压缩、界面-单介质分区计算方法等多个维度出发,综述近几年我们在可压缩多介质流动问题高精度数值模拟方法方面的研究进展。通过上述多个维度的工作,我们建立了一套适用于可压缩多介质流动问题的低耗散、基本无数值振荡的高精度欧拉数值方法,并成功应用于可压缩多介质大变形流动和界面不稳定性诱导湍流混合等问题的数值模拟。相关数值方法研究成果已集成至武器物理等领域工程数值模拟软件中,为相关工程任务提供了重要技术支撑。

In the field of numerical simulation of compressible flows,significant progress has been made in high-resolution shock-capturing schemes.But there are still many numerical challenges in the numerical simulation of compressible multi-material flows involving material interfaces,which are mainly manifested by excessively numerical dissipation and non-physical oscillations across interfaces.The discontinuity of fluid properties at the interface is the main reason for the difficulty of physical modelling and numerical simulating of compressible multimaterial flows.To establish an efficient and high-order numerical algorithm for such flows,five aspects must be considered simultaneously,i.e.,the numerical framework,the compatible discretization of non-conservative equations,the high-order bounded scheme,the interfacecompression,and the multi-region calculation.In this paper we review our works in recent years from these aspects.Through the above-mentioned work,a class of high-order Eulerian numerical simulation methods with low dissipation and essentially non-oscillatory property has been established and successfully applied to interfacial instability and turbulent mixing of compressible multi-material fluids.These numerical methods have been integrated into numerical simulation softwares for engineering problems in weapon physics,and have been providing important technical support for related engineering tasks.