 
Summary: Arch. Rational Mech. Anal. 159 (2001) 229252
Digital Object Identifier (DOI) 10.1007/s002050100158
An Eulerian Description of Fluids Containing
ViscoElastic Particles
Chun Liu & Noel J. Walkington
Communicated by M. E. Gurtin
Abstract
Equations governing the flow of fluid containing viscohyperelastic particles
are developed in an Eulerian framework. The novel feature introduced here is to
write an evolution equation for the strain. It is envisioned that this will simplify
numerical codes which typically compute the strain on Lagrangian meshes moving
through Eulerian meshes. Existence results for the flow of linear viscohyperelastic
particles in a Newtonian fluid are established using a Galerkin scheme.
1. Introduction
When modeling physical systems that contain both fluid and solid particles one
is always confronted with the dilemma that fluids are naturally described using
the Eulerian (spatial) description yet solids are naturally described in a Lagrangian
(referential) frame. From an analysts point of view this decoupling of the problem
presents significant technical challenges. The equation for the fluid takes place on
a timedependent domain (the region not currently occupied by the solid), and the
