三维混合网格高精度守恒积分重映算法研究

In the fields of weapons and inertial confinement fusion, there are many difficulties in their numerical simulation due to high pressure, high temperature and high density ratio. It is a multi-scale and multi-physical coupling complex process and a challenge to high order simulation. The arbitrary Lagrangian-Eulerian (ALE) method is an efficient way in the simulation of complex flows, and has become a frontier theme in the CFD field. Remapping is a key procedure of ALE method. Recently, the three-dimensional conservative remapping is confined by the intersection of tetrahedron, the lower order accuracy for reconstruction and the searching algorithm for donor-grid, which is far from the requirement of practical computation. In this project, the high-order conservative remapping on arbitrary mixed-element (tetrahedral, prismatic, pyramidal and hexahedral elements) unstructured meshes will be developed. We mainly focus on the following three key points: (1) conservative remapping based on the fast intersection of polyhedrons; (2) WENO reconstruction on arbitrary mixed-element unstructured meshes; (3) the efficient searching algorithm for donor-grid based on octree data structure. The project will provide the numerical simulation platform for the lager deformation of CFD, promote the numerical simulation for the flow with complex flow structure and multi-scale physics, and support for the algorithm and program for the practical computation.

武器物理、惯性约束聚变等领域包含着多尺度和多物理耦合等流动现象，在数值模拟这些复杂流体的过程中面临着高温、高压、高密度比等困难。任意拉格朗日欧拉(ALE)方法可有效处理上述难题，是近年来研究的前沿问题之一。重映是 ALE 方法的关键环节。目前，三维积分重映受限于四面体求交、低精度和贡献网格的搜索方法，很难满足实际应用需求。本项目拟研究三维混合网格(含四面体、三棱柱、四棱锥和六面体)高精度守恒积分重映方法，包括以下难点问题：(1) 基于任意多面体快速求交的积分重映研究；(2) 混合网格的高精度加权基本无振荡(WENO)重构；(3) 贡献网格的八叉树搜索算法。本项目将为大变形流体力学的研究搭建高效、实用的数值模拟平台，推动三维复杂流体和多物理过程耦合问题的数值模拟研究工作，为实际工程问题的计算模拟提供算法和程序支撑。

武器物理、惯性约束聚变等领域包含着多尺度和多物理耦合等流动现象，在数值模拟这些复杂流体的过程中面临着高温、高压、高密度比等困难。任意拉格朗日欧拉(ALE)方法可有效处理上述难题，是近年来研究的前沿问题之一。重映是 ALE 方法的关键环节。目前，三维积分重映受限于四面体求交、低精度和贡献网格的搜索方法，很难满足实际应用需求。 本项目研究三维多面体网格(含四面体、三棱柱、四棱锥和六面体)高精度守恒积分重映方法，包含任意多面体快速求交算法、多面体网格高精度加权基本无振荡(WENO)重构、贡献网格八叉树搜素算法。本项目提出一种三维非结构多面体二阶保界全局重映算法。在旧网格上选取模板利用最小二乘构造插值多项式，采用凸包算法计算多面体相交部分，最后使用局部保界修正技术修补重映后的越界量。多项数值实验表明这种格式同时具有高精度、高分辨率和高效率的特点。本项目的研究工作已应用于本单位重点三维数值模拟平台，支撑多个大型程序的考核测试，并为大型程序间提供数据传递支持，推动国产自主三维复杂流体和多物理过程耦合数值模拟软件的发展。