An Efficient and Robust Method for Simulating Two-Phase Gel Dynamics

We develop a computational method 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, which we discretize with finite differences/volumes. The momentum and incompressibility equations present the greatest numerical challenges since i) they involve partial derivatives with variable coefficients that can vary quite significantly throughout the domain (when the phases separate), and ii) their approximate solution requires the "inversion" of a large linear system of equations. For solving this system, we propose a box-type multigrid method to be used as a preconditioner for the generalized minimum residual (GMRES) method. Through numerical experiments of a model problem, which exhibits phase separation, we show that the computational cost of the method scales nearly li...

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Grady B. Wright, Robert D. Guy, Aaron L. Fogelson
• Keywords: Box-type Multigrid Method, Greatest Numerical Challenges, SIAMSC 2008, Transport Equation