A unified finite difference formulation for multiphysics simulations on arbitrary meshes

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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.