Well-balanced and consistent algorithms for three-dimensional simulations of binary immis-cible flows

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With a view to compute three-dimensional multi-component fluid flows in complex geometry encountered in many industrial applications, a novel finite volume method over hybrid unstructured meshes is proposed for the solution of the Navier-Stokes and advection equations. Among the several numerical approaches put forward by various research groups, finite volume method over unstructured meshes offers a promising technique for simulating fluid flow problems in a complex domain. Multi-component fluid flow problems, in particular those involving two fluids distinguished by sharp interface are of practical importance in many engineering applications including mould filling, liquid sloshing, pipeline drainage and fuel injection in an internal combustion engine etc.. Although a considerable amount of work has already been carried out to simulate the multi-component flows, efforts are still going on to handle the complexities associated with different phases. The challenges are mainly due to the jump in fluid properties, the presence of interfacial and large body forces. With the passage of time, a class of algorithms based on force balancing have been evolved. The primary concern of these algorithms is to discretely treat the forcing terms in an identical way. In the recent past, methodologies has been proposed for achieving force balancing over uniform/non-uniform structured meshes, but work on hybrid unstructured meshes is limited.
Supervisor: Amaresh Dalal