复杂构型下多介质流体力学ALE方法

The multi-layered structure media exists in many areas such as inertial confinement fusion (ICF), detonation Physics, elastoplastic physics, astrophysics and the Earth's internal structure. The project will focus on high resolution numerical methods for two-dimensional multi-media and large deformation problems. The main contents are as follows: under the framework of the arbitrary Lagrangian Eulerian (ALE) method, we will research the viscous mechanism which may produce the numerical shock instability, then construct some numerical methods to reduce vorticity errors; We will design a two-dimesional approximate Riemann solver which can keep consistency between a nodal contact velocity and the numerical flux on an edge connected with the node; We will research a new robust ALE method on the two-dimensional cylindrical coordinate system, and keep the numerical solution to preserve the spherical symmtry and conservation simultaneously. We will present a simple and robust contact algorithm for non-matching grid on the multi-media slip interface and hope to improve the accuracy of the numerical method; In addition, a model of interaction among multilayer media under the strong impact of shock will be built, the coresponding computer code adapted to the complex configuration of the flow field will be developed, and numerical simulation of the multilayer interaction of strong shock will be carried out. These works will provide parameters to design experimental device in dynamic high pressure, detonation as well as inertial confinement fusion experiments and establish theoretical basis for radiation transport and detonation equation of state experimental measurements.

在惯性约束聚变、爆轰物理、弹塑性物理、天体和地球内部结构等许多领域中，都涉及到多层介质问题。本项目将针对二维多介质大变形问题，开展高精度高分辨率计算方法研究。主要内容有：在任意拉格朗日欧拉(ALE)方法的框架下，研究导致激波产生数值不稳定性的剪切粘性耗散机制，构造能减少涡度误差的数值方法；设计边界通量与节点接触速度相容的二维近似黎曼解法器，抑制由网格与激波方向不一致而导致的非物理现象；研究实用的二维柱坐标流体力学方程组的ALE方法，解决传统方法守恒性、对称性和健壮性难以兼顾的难题；设计简洁、健壮的接触算法，提高滑移界面非匹配网格上的计算能力。构建强冲击波作用下多层介质相互作用模型，编制相应的计算程序，开展多层介质强激波相互作用的数值模拟；为设计动高压、爆轰以及惯性约束聚变等实验装置提供参数，也为开展辐射输运和爆轰状态方程实验测量奠定理论基础。

本项目针对二维多介质大变形问题，开展了高精度高分辨率计算方法研究。主要内容有：在任意拉格朗日欧拉(ALE)方法的框架下，研究了导致激波产生数值不稳定性的内在机制；设计边界通量与节点接触速度相容的二维近似黎曼解法器，抑制由网格与激波方向不一致而导致的非物理现象；研究实用的二维柱坐标流体力学方程组的ALE 方法；设计了简洁、健壮的接触算法，提高滑移界面非匹配网格上的计算能力。构建强冲击波作用下多层介质相互作用模型，编制了相应的计算程序，开展多层介质强激波相互作用的数值模拟；在强冲击实验的数值模拟中取得了良好的计算效果。