A unified finite difference formulation for multiphysics simulations on arbitrary meshes

任意网格上多物理场仿真的统一有限差分公式

• 批准号: 4484-2011
• 负责人: Barron, Ronald
• 金额: $ 1.46万
• 依托单位: University of Windsor
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568355
• 关键词: unified; finite; difference; formulation; multiphysics

Fluid flows exist throughout nature, in biological systems and in man-made devices. Computational Fluid Dynamics (CFD) is one of the tools that engineers use to predict the behaviour of these complex flows, to gain a deeper understanding of the physical phenomena involved, to improve the performance of fluid devices and to design new ones. The need for user-friendly, reliable, highly accurate and computationally efficient methodologies and algorithms has increased as industries continue to rely more heavily on numerical simulation as a tool to improve their product design. Finite difference methods for the numerical solution of the Navier-Stokes equations were very popular in the early years of CFD development, and still form the basis for many research codes. However, their applicability to flows in complicated and highly irregular domains is severely restricted due to their reliance on structured grid systems. This is the primary reason for the popularity of finite volume solvers, particularly in commercial CFD codes. The aim of this research proposal is to develop an innovative Finite Difference methodology that can be applied to arbitrary meshes, regardless of whether the mesh is structured, unstructured or hybrid, and to multiphysics phenomena. The motivation for this research is the benefits of applying this methodology to real engineering flow problems which, due to their domain complexity, generally require the use of unstructured grids. Advantages of having a finite difference solver for such meshes include the fact that finite difference methods are more efficient than finite volume and finite element methods, are easier to analyze and code, and offer a greater opportunity to achieve more accurate solutions.

流体流动存在于自然界、生物系统和人造设备中。 计算流体动力学 (CFD) 是工程师用来预测这些复杂流动的行为、更深入地了解所涉及的物理现象、提高流体设备的性能和设计新设备的工具之一。 随着行业继续更加依赖数值模拟作为改进产品设计的工具，对用户友好、可靠、高精度和计算高效的方法和算法的需求不断增加。 用于纳维-斯托克斯方程数值求解的有限差分方法在 CFD 发展的早期非常流行，并且仍然构成许多研究代码的基础。 然而，由于它们对结构化网格系统的依赖，它们对复杂和高度不规则域中的流动的适用性受到严重限制。 这是有限体积求解器流行的主要原因，特别是在商业 CFD 代码中。 本研究提案的目的是开发一种创新的有限差分方法，该方法可应用于任意网格（无论网格是结构化、非结构化还是混合）以及多物理现象。 这项研究的动机是将这种方法应用于实际工程流程问题的好处，由于其领域的复杂性，通常需要使用非结构化网格。 对于此类网格使用有限差分求解器的优点包括：有限差分方法比有限体积和有限元方法更有效，更易于分析和编码，并且提供了获得更准确解决方案的更大机会。