We 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 volumeaveraged 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.
Du, Jian; Fogelson, Aaron L.; and Wright, Grady. (2008). "A Parallel Computational Method for Simulating Two-Phase Gel Dynamics". International Journal for Numerical Methods in Fluids, 60(6), 633-649. http://dx.doi.org/10.1002/fld.1907