复杂地质模型六面体网格几何自适应重划分方法研究

The degenerated computational mesh models caused by large-deformations in numerical simulation can lead to the termination of numerical calculation. The remeshing of the degenerated mesh models is an effective manner to deal with the above problem. Aiming at the degenerated hexahedral meshes caused by the large-deformations in engineering geological simulations, this project proposes to first develop an effective approach to fast locate the degenerated hexahedrons and automatically determine the local degenerated region, and then design an effective, geometrically adaptive algorithm for remeshing the local degenerated regions with the consideration of the complex geological structures and human activities, and finally develop a valid mesh optimization method that is capable of significantly improving the mesh quality while preserving geological and geometrical features of the computational mesh models. The objective of this research project is to develop an effective and adaptive approach to remeshing the degenerated hexahedral mesh models caused by the large-deformations in engineering geological simulations. Moreover, this project attempts to accelerate the remeshing of the degenerated hexahedral meshes on the GPU on the basis of analyzing the features of modern GPU. The motivation of speeding up the remeshing is to significantly improve the efficiency of the adaptive remeshing process, while being able to generate and provide high-quality hexahedral mesh models to be used in the numerical analysis of the large-deformation problems in engineering geology. The research results of this project are of great interest to realizing the simulation of large-deformation of rock and soil masses and improving the computational efficiency and accuracy, and are capable of providing a guide on the remeshing of hexahedral meshes generated from non-geological models composing of multiple materials.

数值模拟中因发生大变形导致的计算网格畸变会造成模拟计算终止，网格重划分是解决上述问题的有效方法。本项目拟针对岩土体大变形模拟中、基于复杂地质模型的畸变六面体网格，首先研究畸变单元的快速判别方法和畸变区域的自动确定方法，再通过综合考虑地质构造和人工活动等地质模型的特征，研究具有多介质多属性特征的畸变区域的几何自适应重划分方法，并探索能够保持计算网格多介质多属性特征和地质模型几何特征的网格优化方法，最终形成面向多介质多属性特征的复杂地质模型的六面体网格几何自适应重划分方法，以期为大变形的模拟提供高质量的六面体网格。同时，本项目拟通过分析可编程GPU的并行计算特征，研究能够加速六面体重划分的并行策略及方法，以期在能够提供高质量六面体网格的同时，显著提高重划分效率。本项目对实现岩土体大变形的模拟和提高大变形模拟的精度及效率有重要意义，且可以为具有多介质多属性特征的非地质模型的六面体重划分提供思路。

复杂地质模型的高质量计算网格是分析岩土体变形和破坏的关键。当采用有限元或有限差分方法分析岩土体大变形及破坏时，计算网格会出现较大变形，甚至出现大量畸变单元，这将导致数值计算失败。为实现对岩土体如复杂边坡的变形破坏的连续模拟，本项目研究了复杂地质模型的几何自适应重划分方法。完成的主要研究工作如下：基于计算几何算法库（CGAL），研制了用于生成高质量计算网格的程序包；提出了考虑不同数据布局和迭代形式影响的三维拉普拉斯光滑的GPU加速并行算法，实现了大规模计算网格的质量优化；基于多核CPU和众核GPU，提出了针对大规模有限元计算网格的、高效、并行合并及清理算法；形成了基于网格自适应重划分的边坡破坏FDM模拟方法，实现了对边坡变形破坏的连续模拟；形成了基于网格自适应重划分的开采沉陷FDM模拟方法，解决了开采沉陷诱发的岩层大变形模拟问题。这些方法和算法的研究，着眼于实际应用瓶颈问题的解决，在实现岩土体大变形及破坏的高可信数值模拟上具有重要意义。