A parallel computational method for simulating two‐phase gel dynamics on a staggered grid

Abstract

SUMMARYWe develop a parallel computational algorithm for simulating models of gel dynamics where the gel is described by two phases, a networked polymer and a fluid solvent. The models consist of transport equations for the two phases, two coupled momentum equations, and a volume-averaged incompressibility constraint. Multigrid with Vanka-type box-relaxation scheme is used as preconditioner for the Krylov subspace solver (GMRES) to solve the momentum and incompressibility equations. Through numerical experiments of a model problem, the efficiency, robustness and scalability of the algorithm are illustrated.

A high-resolution finite-difference method for simulating two-fluid, viscoelastic gel dynamics

“…The method we use for solving (26) is based on the preconditioned Krylov subspace method first introduced for gels in [9] and developed further in [10,11]. The gel model considered in these studies was for two immiscible viscous-dominated fluids and did not contain inertial effects.…”

A Cartesian grid method for two‐phase gel dynamics on an irregular domain

“…It is shown in [13] that the multigrid-preconditioned GMRES procedure is robust and efficient even when sharp gradients in volume fraction develop during the gel separation process. A parallel version of the algorithm is developed in [20].…”