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

Explore a comprehensive lecture on bound-preserving numerical solutions for variable density two-phase flows in this one-hour Society for Industrial and Applied Mathematics presentation. Delve into the importance of pore-scale flow modeling for energy and environmental applications, focusing on phase-field models that implicitly track interfaces between phases and handle contact line motion. Learn about an efficient numerical method for solving phase-field models characterized by coupled Cahn-Hilliard and Navier-Stokes equations for phases with different densities. Discover the use of discontinuous piecewise polynomials for approximating unknowns and a splitting method for incompressible Navier-Stokes equations. Understand the implementation of flux and slope limiters to eliminate bulk shift, overshoot, and undershoot in the order parameter, ensuring bound preservation. Examine numerical examples including spinodal decomposition, flows in micro-structures, and flows in digital rocks. Gain insights into energy dissipation, diffuse interface parameters, and open questions in the field from expert speaker Beatrice Riviere of Rice University.