Recent advances in discontinuous Galerkin discretization of Cahn–Hilliard–Navier–Stokes models for systems of two-phase flows

Speaker: Chen Liu (Purdue)
Dates: 2023/10/26
Location: Zoom, link
Abstract: Efficient and accurate pore-scale fluid dynamics simulators have important applications in digital rock physics. One of the popular approaches for modeling two-phase fluid flow in micro-to-millimeter pore structures is to use phase-field equations. This talk presents recent advances in the discretization of phase-field models for systems of two-phase flows, characterized by coupled Cahn–Hilliard and Navier–Stokes equations. We first focus on the analysis of an energy-stable discontinuous Galerkin algorithm for solving the Cahn–Hilliard–Navier–Stokes (CHNS) equations within a decoupled splitting framework. Next, we show for time-dependent partial differential equations, the numerical schemes can be rendered bound-preserving without losing conservation and accuracy, by a postprocessing procedure of solving a constrained minimization in each time step. Such a constrained optimization can be formulated as a nonsmooth convex minimization problem, which can be efficiently solved by Douglas–Rachford method if using the optimal algorithm parameters. Numerical tests on a CHNS system indicate that our algorithm is high-order accurate, very efficient, and well-suited for large-scale 3D simulations in complex computational domains.