The main aim of my research has been to develop efficient and accurate techniques for the solution of computational fluid dynamics (CFD) problems in real life geometries. The approach taken has been to extend the Finite Volume approach (FV), which offers a highly efficient solution procedure on Cartesian meshes, to handle the unstructured meshes required to represent the geometries present in engineering applications. The resulting software has been used in a wide range of application areas but has been primarily employed to simulate processes within metals processing industries. These processes require the solution of not only CFD but also may involve structural deformation, electro-magnetic effects, particulate phases, chemical reactions and radiation effects all off which have been resolved in a single software framework.

The principle approach I’ve taken to extend the FV method to unstructured meshes has been based on the collocated cell centred technique. The extension of this method to unstructured meshes results in an efficient solution procedure, when compared with other unstructured mesh methods, but the accuracy is affected by both the mesh quality and the need to estimate face fluxes from elemental values. Developments in both these areas have improved the accuracy of the approach but there are still bounds to its applicability. I have been involved in the supervision of PhD projects that have investigated the coupling of vertex based FV, which handles unstructured meshes very well but is not very efficient, with cell centred FV to offer a staggered approach to the hydrodynamics and also the use of multi-grid techniques in parallel and their application using unstructured meshes.

I have applied the numerical models to a number of application areas. The first of these applications was the modelling of the gaseous topspace above the metal bath in the HISmelt process (continuous iron smelting). The model included the resolution of anisotropic turbulent, swirling flows, chemical reactions and radiation effects and the coupling between the continuum gaseous phase and a number of particulate phases that were ‘erupted’ from the metal bath. A recurring strand has been the simulation of casting applications. This has included the simulation of directional solidification, investment, continuous and centrifugal casting. Simulation of these processes requires the inclusion of free surface, solidification and structural mechanics algorithms which, with the exception of the structural deformation, I have been involved with implementing.

Current and recent projects and research areas include:

1. centrifugal casting in association with Rolls Royce and the University of Birmingham
2. continuous casting with Arcelor-Mittal and the University of Greenwich
3. coal delivery systems with Corus – Port Talbot
4. water turbines funded by WERC
5. water treatment processes

Recent Journal Papers

• “An alternative mixed Eulerian Lagrangian approach to high speed collision between solid structures on parallel clusters”,  A.K. Slone, T.N. Croft, A.J. Williams and M. Cross, Advances in Engineering Software, 38:4, pp 244-255, 2007
• “A coupled finite volume method for the solution of flow processes on complex geometries”, D.McBride, T.N. Croft and M. Cross, International Journal for Numerical Methods in Fluids, 53, pp 81-1004, 2007
• “Finite volume method for the solution of flow on distorted meshes”,  D.McBride, T.N. Croft and M. Cross, International Journal for Numerical Methods in Heat and Fluid Flow, 17:2, pp 213-239, 2007
• “Computational modelling of bubbles, droplets and particles in metals reduction and refining”, M. Cross, T. N. Croft, G. Djambazov and K.Pericleous, Applied Mathematical Modelling, 30:11, pp1445-1458, 2006
• “Computational fluid dynamics: Advancements in Technology for modeling Iron and steelmaking processes”, M. Cross, T. N. Croft, D. McBride, A. K. Slone and A. J. Williams, AIST Transactions, 3:7, pp 155-163, 2006
• “A group based solution strategy for multi-physics simulations in parallel”, A. J. Williams, T. N. Croft and M. Cross, Applied Mathematical Modelling, 30:7, pp 656-674, 2006
• “Computational modelling of variably saturated flow in porous media with complex three--dimensional geometries”, D. McBride, M. Cross, N. Croft, C. Bennett and J. Gebhardt, International Journal for Numerical Methods in Fluids, 50, 1085-1117, 2006
• “Computational modeling of reactive multi-phase flows in porous media: Applications to metals extraction and environmental recovery processes”, M. Cross, C.R. Bennett, T.N. Croft, D. McBride and J.E. Gebhardt, Minerals Engineering, 19:10, 1098-1108, 2006
• “Computational Modeling of Mold Filling and Related Free-Surface Flows in Shape Casting: An Overview of the Challenges Involved”, M. Cross, K. Pericleous, T.N. Croft,  D. McBride, J.A. Lawrence and A.J. Williams, Metallurgical and Materials Transactions B, 37B, 879-886, 2006
• “Assessing the parallel performance of multi-physics tools for modelling of solidification and melting processes”, K. McManus, A. J. Williams, M. Cross, T. N. Croft and C. Walshaw, International Journal of High Performance Computing Applications, 19:1, 1-27, 2005