High-order Geometry, Mesh and Adaptivity for Fluid-Structure Interaction Simulations

流固耦合仿真的高阶几何、网格和自适应性

• 批准号: RGPIN-2020-06327
• 负责人: Guibault, François
• 金额: $ 2.84万
• 依托单位: École Polytechnique de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=740749
• 关键词: order; Geometry; Mesh; Adaptivity; Fluid

During the last decades, very significant advances have been made in the field of domain representation and discretization for the purpose of simulation-based engineering sciences. These developments have been mostly based on linear representations of domain boundaries and space discretization using low-order elements. Recently, very significant developments have been made towards p-version finite element analysis (FEA), isogeometric analysis (IgA) and high-order (HO) simulations, for several types of partial differential equations, and in particular for structural problems. In these new approaches, HO elements and shape functions are used, thereby increasing the number of degrees of freedom supported by each discrete element, and spatial discretization of boundaries are represented by high degree interpolants that preserve the accuracy of the geometric shapes modeled using CAD systems. Significant reduction in the number of elements and overall computational cost may be achieved, while increasing solution accuracy. A similar trend may be observed in the field of computational fluid dynamics (CFD), where HO methods for fluid flow simulations are also gaining momentum, especially in LES and DNS-type simulations, using various types of Finite Element discretization approaches. A natural extension to these single-discipline advancements involves the development of multi-physics simulation methodologies to model, for instance, the interaction between fluids and solids (FSI). This progress is however hampered by the need for high-quality and robust spatial discretization approaches to generate curved elements which are adapted to the specific features of the physical phenomena being simulated. This research program aims to contribute to the promotion and penetration of HO methods in the practice of engineers and scientists through the development of efficient and robust HO mesh generation and manipulation methods and their validation on test cases representative of real-world applications.

在过去的几十年里，基于仿真的工程科学在领域表示和离散化方面取得了非常显著的进展。这些发展主要基于域边界的线性表示和使用低阶元素的空间离散化。最近，对于几种类型的偏微分方程，特别是结构问题，在p型有限元分析（FEA），等几何分析（IgA）和高阶（HO）模拟方面取得了非常重要的进展。在这些新方法中，使用了HO元素和形状函数，从而增加了每个离散元素支持的自由度数量，并且边界的空间离散化由高阶插值表示，从而保持了使用CAD系统建模的几何形状的准确性。在提高求解精度的同时，可以实现元素数量和总体计算成本的显著减少。在计算流体动力学（CFD）领域也可以观察到类似的趋势，其中流体流动模拟的HO方法也获得了动力，特别是在LES和dns类型的模拟中，使用各种类型的有限元离散化方法。这些单一学科进步的自然延伸涉及多物理场模拟方法的发展，例如，流体和固体之间的相互作用（FSI）。然而，由于需要高质量和鲁棒的空间离散化方法来生成适应所模拟物理现象的特定特征的弯曲元素，这一进展受到阻碍。本研究计划旨在通过开发高效、稳健的HO网格生成和操作方法，以及在代表现实世界应用的测试用例上进行验证，促进HO方法在工程师和科学家实践中的推广和渗透。