Vertex-based discretisation methods for thermo-fluid flow in a finite volume-unstructured mesh context
The main aim of this research project is to investigate techniques to improve the resolution of flow variables on unstructured skewed meshes whilst working within a Finite Volume (FV) context. A three-dimensional vertex-based FV algorithm for the solution of thermo- fluid flow problems has been developed and integrated within a multi-physics FV framework PHYSICA. Currently PHYSICA employs a cell-centred discretisation technique for fluid mechanics problems and a vertex-based discretisation technique for solid mechanics problems. The vertex-based discretisation approach is validated for a variety of heat transfer problems and comparisons are made with cell-centred solutions. A coupled thermo-mechanical problem, including solidification and radiation, is simulated using vertex-based and cell-centred techniques. Results, run-time and memory requirements are compared. Hybrid vertex-based/cell-centred discretisation of the hydrodynamic variables is also investigated. The components of velocity are solved vertex-based with pressure cell-centred or conversely pressure is solved vertex-based with velocity cell-centred. The methods are applied to flow in a lid-driven cavity and solutions are obtained on a number of distorted meshes. Comparisons are made with the benchmark solutions. The hybrid discretisation enables solutions on distorted meshes where purely cell-centred techniques fail. The hybrid methods produce final solutions containing errors due to mesh distortion. The co-located vertex-based flow solutions obtained on the distorted meshes are comparable to solutions obtained on a uniform Cartesian mesh. Having a good resolution of the flow field on distorted meshes enables the solution of other transported variables using cell-centred techniques. Finally, this hybrid vertex-based/cell-centred technique is applied to thermally driven flow, turbulent flow, and three-dimensional flow over an aircraft wing.