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.

流体流动存在于整个自然界、生物系统和人造装置中。 计算流体动力学（CFD）是工程师用来预测这些复杂流动行为的工具之一，以更深入地了解所涉及的物理现象，提高流体设备的性能并设计新设备。 对用户友好的，可靠的，高精度和计算效率的方法和算法的需求已经增加，因为行业继续更严重地依赖于数值模拟作为一种工具，以改善他们的产品设计。 在CFD发展的早期，数值求解Navier-Stokes方程的有限差分方法非常流行，并且仍然是许多研究代码的基础。 然而，由于它们依赖于结构化网格系统，它们对复杂和高度不规则域中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。 这项研究的目的是开发一种创新的有限差分方法，可以应用于任意网格，无论网格是结构化的，非结构化的或混合的，以及多物理现象。 这项研究的动机是将这种方法应用于真实的工程流问题的好处，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，更容易分析和编码，并且提供了更大的机会来实现更准确的解决方案。