Unstructured staggered mesh discretisation methods for computational fluid dynamics

Abstract

There are many branches of engineering science that require solution of fluid flow problems. Some of these examples are aerodynamics of aircraft and vehicles, hydrodynamics of ships, electrical and electronic engineering and many others. Some of these flows may involve complex geometrical shapes which are usually modelled using the unstructured mesh discretisation techniques. There are well established methods that are used in such simulations. The aim of this project is to investigate the staggered positioning of variables on an unstructured based context and hence compare it to well known methods such as the cell-centred approach. A two dimensional unstructured staggered mesh discretisation method for the solution of fluid flow and heat transfer problems has been developed. This method stores and solves the vector variables at the cell faces and other scalar variables are stored at the cell centres. The very well known pressure based scheme SIMPLE is employed for pressure and velocity coupling. Three different approaches on unstructured staggered meshes are proposed. The first method solves for normal velocity component and interpolates the tangential velocity component, the second method solves for normal and tangential velocity components whereas the third method also solves for normal and tangential velocity components but uses a different upwind scheme for convection. The discretisation on unstructured staggered mesh methods is validated for a variety of fluid flow and heat transfer problems and comparisons are made between unstructured staggered mesh methods, the cell-centred approach and benchmark solutions. The first and third unstructured staggered mesh methods are shown to perform well and give comparable results to benchmark solutions. The third unstructured staggered mesh method does not always work