基于网格局部重连技术的相容ALE方法

Large deformations of fluid interfaces due to the strong interactions between different materials often appear in a variety of science and engineering problems, such as weapon physics, ICF, astrophysics. ALE is one of the most popular numerical methods for simulation of multimaterial fluid dynamics with large deformations. But existing ALE methods have several shortcomings. 1) Mesh velocities are not compatible with numerical fluxes. This leads to non-physical mesh distortions, numerical shock instabilities and other numerical errors. 2) Topology-invariant mesh rezoning can not be used for large deformation problems. 3) Computation of intersections of mesh cells are necessary for conservative remapping. In this project, we will mainly study compatible ALE methods based on mesh reconnections: 1) Compatible ALE method in which velocity of mesh is compatible with numerical fluxes; 2) Rezoning algorithms based on unstructured mesh reconnections; 3) Remapping algorithms without computation of intersections between the cells of old mesh and the cells of new mesh.

在武器物理、惯性约束聚变（ICF）、天体物理等国防和前沿科学工程领域的物理问题经常遇到多种物质强相互作用导致的物质界面大变形。ALE方法是模拟多介质大变形流体力学问题常用的数值方法之一。现有ALE方法存在以下缺陷：1）网格节点速度和数值通量不相容，导致网格非物理扭曲，数值激波不稳定等现象；2）基于拓扑不变的网格重分方法难以处理界面大变形问题；3）守恒重映需要新旧网格单元求交，难以推广到高精度。本项目主要研究基于网格局部重连技术的相容ALE方法，克服上述缺陷：1）节点速度和数值通量相容的ALE方法；2）基于非结构网格局部重连技术的重分方法；3）无需单元求交的高精度守恒重映方法。

本项目针对武器物理、ICF以及天体物理中的多介质大变形问题，开展了基于网格局部重连技术的ALE计算方法研究。主要内容有：1.二维和轴对称二维相容ALE算法；2.轴对称问题的高精度数值方法；3.非结构三角形网格的质量准则；4. 保持物质界面的局部重连算法和物理量重映算法；5. 编制相应计算程序并进行了数值验证。