@Article{CiCP-14-1322,
author = {Jian Du, Robert D. Guy, Aaron L. Fogelson, Grady B. Wright and James P. Keener},
title = {An Interface-Capturing Regularization Method for Solving the Equations for Two-Fluid Mixtures},
journal = {Communications in Computational Physics},
year = {2013},
volume = {14},
number = {5},
pages = {1322--1346},
abstract = {<p style="text-align: justify;">Many problems in biology involve gels which are mixtures composed of
a polymer network permeated by a fluid solvent (water). The two-fluid model is a
widely used approach to described gel mechanics, in which both network and solvent
coexist at each point of space and their relative abundance is described by their volume
fractions. Each phase is modeled as a continuum with its own velocity and constitutive law. In some biological applications, free boundaries separate regions of gel and
regions of pure solvent, resulting in a degenerate network momentum equation where
the network volume fraction vanishes. To overcome this difficulty, we develop a regularization method to solve the two-phase gel equations when the volume fraction of
one phase goes to zero in part of the computational domain. A small and constant
network volume fraction is temporarily added throughout the domain in setting up
the discrete linear equations and the same set of equation is solved everywhere. These
equations are very poorly conditioned for small values of the regularization parameter, but the multigrid-preconditioned GMRES method we use to solve them is efficient
and produces an accurate solution of these equations for the full range of relevant regularization parameter values.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.180512.210313a},
url = {http://global-sci.org/intro/article_detail/cicp/7204.html}
}