Fast Numerical Methods and Software for Phase-Field Simulation of Multiphase Flow Problems

Phase-field models allow multiple phases to be represented via the introduction of one or more artificial phase variables alongside the usual physical flow variables. Typically, a value of 0 indicates absence of that phase at a given point whilst a value of 1 indicates that the phase occupies that point fully. The interface between phases is modelled as a narrow region, where the phase value varies smoothly between 0 and 1, rather than a sharp interface. This approach is extremely flexible for modelling complex multi-phase flows – though at the expense of introducing additional dependent variables and additional PDEs. This project will develop and implement state-of-the-art numerical methods to allow three-dimensional, time-dependent multiphase flow problems to be tackled in an efficient manner using the phase-field approach. The novel contributions will take the form of the development and application of new computational algorithms to allow optimal efficiency in the solution of these problems – including mesh refinement at the phase interfaces and a solver with optimal computational complexity. This will allow a range of complex multiphase flow applications to be solved with higher levels of accuracy, resolution and efficiency that is currently possible.