Generic and robust numerical framework for multiphase flows using volume-of-fluid/immersed boundary methods

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The thesis presents the development of a multi-fluid/multiphase flow solver for numerical simulations involving immiscible and miscible fluid flows with large density ratios interacting with multiple stationary and/or moving rigid solids. We discuss the development of a two-dimensional, incompressible, finite volume solver employing a novel hybrid staggered/non-staggered framework wherein a single normal momentum equation is solved at the cell faces. The framework then integrates several strategies, based on the volumeof- fluid method in a unified manner, to simulate multi-fluid/multiphase flows those are frequently encountered in practical and engineering applications. We first propose generic guidelines for the development of interface capturing schemes for accurate resolution of interfaces between immiscible fluids. These guidelines are used to devise two new interface capturing schemes and their capability is analysed in typical advection tests where they are found to be as good as and sometimes even superior to existing schemes on structured and unstructured meshes. Subsequently, these schemes are coupled with the normal momentum equation in the hybrid staggered/non-staggered framework for multi-fluid simulations and preliminary validation studies are carried out. However, fluid flows with large density ratios are prone to numerical instabilities which often arise in surface tension and gravity dominated flows.
Supervisor: Ganesh Natarajan