基于大变形流场涡量特征的自适应ALE方法研究

Simulations of multimaterial flows with complex deformation have always been a difficult and essential problem in the field of weapon and inertial confinement fusion research, in which ALE methods play dominant roles. However the ALE methods still face difficulties in the accuracy and confidence in some cases of large deformation. The fidelity of its simulation results is not guaranteed and may lead to great difficulties for the physical analysis and algorithm design. The large deformation flow is a kind of multi-dimensional flow essentially. Its characteristics lie in the vorticity generation and evolution which are often neglected in the traditional compressible hydrodynamic numerical methods. Therefore this project aims at (1) investigating the cause of spurious mesh deformation and the corresponding numerical difficulties in the view of vorticity and constructing a vorticity-preserving cell-centered hydrodynamic Lagrangian method free of such mesh imprinting; (2)developing adaptive mesh remapping and optimizing technique based on a prior measurement of vorticity to evaluate the flow field deformation degree. This research will develop vorticity preserving Lagrangian methods and adaptive mesh generation method based on the vorticity to improve the fidelity of ALE methods in simulating large-deformation multimaterial flows. It is expected that such a research provides highly reliable numerical tools for CFD and related engineering problems.

在武器物理和惯性约束聚变等国防科技领域，多介质复杂流动问题的数值模拟是一个困难且重要的关键问题。任意拉氏-欧拉方法（ALE）是这类问题的主要算法，然而在流场大变形情况下其模拟的精度和置信度一直存在诸多问题，给物理分析和程序算法带来了很大困难。大变形流动本质是一个多维流动，显著特征在于涡量的生成和演化，传统方法往往忽略了这一方面特性。为此，本项目拟开展如下工作：（1）从涡量运动的角度分析大变形产生的物理机制和数值模拟困难，构造保持流场涡量特征的中心型拉氏方法，抑制传统方法常见的虚假网格变形。（2）提取流场涡量以度量大变形的发展程度，据此自适应地进行网格重分和优化。本项目通过发展有涡量保持性质的拉氏格式和涡量自适应网格重分和优化技术，可提升ALE方法对多介质大变形问题的数值模拟置信度。本项目研究可为工程应用中的复杂流动数值模拟提供方法和理论支撑。

本项目重点研究了大变形流动的多维机制，取得如下创新成果:.针对二维欧拉方程组，(1)在二维广义黎曼问题（GRP）理论研究方面取得了特别创新的成果，建立了可解析求解的非线性二维弱耦合GRP理论模型，给出了解的具体表达形式，由此形成了具有真正二维特性的WGRP解法器，并在数值格式上得到了应用，显示出考虑切向作用的必要性。(2)提出了一种具有涡量自适应节点解法器的满足几何守恒律的高阶中心型拉氏格式（LAVANS格式）。(3)首次将流体力学基本过程理论应用于ALE方法中，给出了基于广义LAMB矢量旋度的自动化网格重分判据，并在ICF应用中取得显著效果。(4)提出了基于非结构网格的三阶WENO方法，既在几何品质较差网格上获得预期的精度，又对强间断问题具有鲁棒性。.针对二维可压缩N⁃S方程，进行了多个不可压和可压缩单模多模瑞利泰勒不稳定性问题的比算研究，既比较了两个程序的数值性能，又给出了运动粘性系数和网格尺度的关系。.针对二维不可压缩N⁃S方程，提出了同时满足任意速度边界条件和不可压条件的最优动力系统的建模方法，并进行了相应的动力学分析。.课题组参加1项国际合作，1次国际会议，2次国内受邀报告，发表4篇高质量的学术论文，1篇国防科技报告，1篇专项归档报告。