Gravity currents comprise of a wide range of natural phenomena which take place in the atmosphere and the oceans. The mechanics of gravity currents have been thoroughly investigated in the past, but only recently have the compu- tational resources accessible to researchers provided the suitable conditions for examining the details of the fluid dynamics of these phenomena in more complex configurations. The first part of this work entails the prediction of gravity currents which flow through straight channels. This kind of analysis has been extensively investigated in the past, however, differently from the existing research, the effects induced by the impulsive vertical removal of a lock-gate at the interface between the dense and the ambient fluid are examined here for the first time. Despite the fact that numerical studies are often concerned with lock-release density currents, the triggering mechanism which occurs in the early stages of the evolution of the fluid flow has always been neglected. In addition, the interaction between the free surface at the top of the ambient fluid and the density current itself is inspected. The additional physics included in the model leads to greatly improved accuracy of the numerical simulation and provides a very detailed insight into the dynamics associated with the interaction between the density current, the free surface and the moving lock-gate. The second part concerns the modelling of saline gravity currents through three-dimensional submerged channels. In particular, the pattern of 'secondary circulation at the bend apexes of sinuous channels is investigated in order to clarify the contradictory observations which have been highlighted by different workers. The debate as to whether the cross-stream circulation produced by the passage of a gravity current occurs in the same way as in a river (e.g. Imran et al. 2004; Islam & Imran, 2008a) or in a reversed fashion compared to that of a river (e.g. Keevil et al., 2006; Peakall et al., 2007) has been ongoing since 2006. In this thesis an attempt is made to provide an explanation which incorporates and unifies these apparently contradictory results,.

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.

A Large Eddy-Simulation code, based on a mesh transparent algorithm, for hybrid unstructured meshes is presented to deal with complex geometries that are often found in engineering flow problems. While tetrahedral elements are very effective in dealing with complex geometry, excessive numerical diffusion often affects results. Thus, prismatic or hexahedral elements are preferable in regions where turbulence structures are important. A second order reconstruction methodology is used since an investigation of a higher order method based upon Lele's compact scheme has shown this to be impractical on general unstructured meshes. The convective fluxes are treated with the Roe scheme that has been modified by introducing a variable scaling to the dissipation matrix to obtain a nearly second order accurate centred scheme in statistically smooth flow, whilst retaining the high resolution TVD behaviour across a shock discontinuity. The code has been parallelised using MPI to ensure portability. The base numerical scheme has been validated for steady flow computations over complex geometries using inviscid and RANS forms of the governing equations. The extension of the numerical scheme to unsteady turbulent flows and the complete LES code have been validated for the interaction of a shock with a laminar mixing layer, a Mach 0.9 turbulent round jet and a fully developed turbulent pipe flow. The mixing layer and round jet computations indicate that, for similar mesh resolution of the shear layer, the present code exhibits results comparable to previously published work using a higher order scheme on a structured mesh. The unstructured meshes have a significantly smaller total number of nodes since tetrahedral elements are used to fill to the far field region. The pipe flow results show that the present code is capable of producing the correct flow features. Finally, the code has been applied to the LES computation of the impingement of a highly under-expanded jet that produces plate shock oscillation. Comparison with other workers' experiments indicates good qualitative agreement for the major features of the flow. However, in this preliminary computation the computed frequency is somewhat lower than that of experimental measurements.