Development of CFD Cut-Stencil Technology for Highly Complex Domains

复杂的流体流动存在于自然界、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。流体经常与其他介质相互作用，这些介质的行为受其他物理特性的支配。这些相互作用的数学建模称为多物理场建模。随着工业继续更多地依赖数值模拟作为改进其产品设计的工具，对多物理场现象的用户友好、可靠、高保真和计算效率的方法和算法的需求有所增加。

Complex 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. Fluids often interact with other media whose behaviour is governed by other physics. The mathematical modelling of these types of interactions is referred to as multiphysics modelling. The need for user-friendly, reliable, high-fidelity and computationally efficient methodologies and algorithms for multiphysics phenomena 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. 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 a unified approach that leads to an innovative, robust Finite Difference methodology for the numerical simulation of multiphysics phenomena that can be applied to arbitrary meshes, regardless of whether the mesh is structured, unstructured or hybrid, or the domain is covered by a cloud of points. Advantages of having a finite difference solver for such meshes include the fact that they are more efficient than finite volume and finite element methods, are easier to analyze and code, and offer a greater opportunity to achieve high-order accurate solutions with relatively little additional cost.