Bound-Preserving Numerical Solutions of Variable Density Two-Phase Flows

This course aims to teach learners how to efficiently solve phase-field models for variable density two-phase flows using numerical methods. The course covers approximating unknowns with discontinuous piecewise polynomials, using a splitting method for the Navier-Stokes equations, and applying flux and slope limiters to eliminate bulk shift in the order parameter. The teaching method involves a detailed description of the numerical techniques used, along with practical examples such as spinodal decomposition and flows in micro-structures. This course is intended for individuals interested in modeling pore-scale flows for applications related to energy and the environment.