Geometry, mesh and adaptivity for high reynolds number viscous flow simulations

虽然数值方法和CFD在过去二十年中取得了巨大的进步，但它们对高度复杂工业问题的适用性仍然受到工程师精确建模和离散计算域所需的努力和时间的限制。提出的研究旨在通过开发创新的几何和网格操作方法来解决仿真需求，帮助减少工程师准备模型所需的时间。本研究项目还旨在提高高雷诺数湍流计算流体动力学（CFD）分析用于复杂三维机械装置，特别是水力涡轮机械设计的准确性和精密度。本提案将研究以下创新方法：1)几何建模，2)网格生成，以及3)在使用有限体积求解器进行粘性湍流不可压缩流CFD模拟的背景下进行后置网格自适应。提出的几何建模研究旨在提高计算域的表示和操作。本研究将探讨计算域的隐式和标准参数边界表示的结合，以便利用每种表示在域离散化和形状处理方面的互补优势。将特别研究表面再参数化技术，通过使用替代表示来构建替代表面，以支持随后的领域离散化操作。网格生成的研究将集中在先验地构建适当的单元尺寸和形状控制函数，以有效地生成高质量的计算网格。在工业应用中，非结构化网格生成过程中单元形状和尺寸的控制是许多困难的根源。提出的研究将旨在确定适用于混合单元类型网格的有效尺寸规范方法。与后验网格自适应相关的主题包括不可压缩湍流Navier-Stokes有限体积解的后验误差估计，几个变量的组合来引导自适应和网格自适应算法的收敛性。

While numerical methods and CFD have progressed tremendously in the last twenty years, their applicability to highly complex industrial problems is still limited by the efforts and time required by engineers to accurately model and discretize computational domains. The proposed research aims to help reduce the time required by engineers to prepare models through the development of innovative geometry and mesh manipulation methods addressing the needs of simulation. This research program also aims to enhance the accuracy and precision of high Reynolds number turbulent computational fluid dynamics (CFD) analysis used for the design of complex three dimensional mechanical devices, and particularly hydraulic turbomachinery. This proposal will investi- gate innovative approaches for 1) geometric modeling, 2) mesh generation and 3) a posteriori mesh adaptation in the context of CFD simulations of viscous, turbulent incompressible flows using finite volume solvers. The proposed research on geometric modeling aims to advance computational domain representation and manipula- tion. This research will investigate combining implicit and standard parametric boundary representation of a computational domain in order to benefit from complementary advantages of each representation for domain discretization and shape manipulation. Surface reparameterization techniques will be particularly investigated, through the construction of surrogate surfaces using alternate representations in support to subsequent domain discretization operations. Research on mesh generation will focus on the a priori construction of adequate el- ement size and shape control functions for the efficient generation of high quality computational grids. Control of element shape and size in the course of unstructured mesh generation is the source of many difficulties in the context of industrial applications. The proposed research will aim to identify efficient size specification approaches applicable to meshes of mixed element types. Themes related to a posteriori mesh adaptation include a posteriori error estimation for incompressible turbulent Navier-Stokes finite volume solutions, the combination of several variables to steer adaptation and convergence of mesh adaptation algorithms.