The understanding of bubble nucleation, growth, and collapse has many practical applications ranging from nuclear to naval and even space. For example, high efficiency nuclear stations, which include cooling systems with high pressure two-phase flows, could be improved through the modeling of vapour-gas interactions. Because of this widespread applicability, ongoing research to develop efficient, high-accuracy algorithms and software to solve complex simulation scenarios of three-dimensional vapour bubble interactions with their surrounding fluid has significant implications.This thesis proposes an efficient approach to solving flow problems accurately (with an emphasis on two-phase flow) by applying discrete exterior calculus to a vorticity based method. To solve flow problems computationally, they must be resolved at a discrete level with minimal loss in accuracy. As discrete exterior calculus applies differential and integral calculus of vector functions to a discrete model, it is ideally suited to building discrete mathematical operators such as Grad, Curl, Div and Laplace directly, resulting in sparse matrix operators that are computationally efficient. The proposed approach bridges the gap between the engineering discipline and discrete exterior calculus, a commonly overlooked mathematical field that is ideally suited for solving complex problems in a discrete domain. Furthermore, through the use of the vorticity formulation of the Navier-Stokes equations, this discrete model intrinsically preserves angular momentum.
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