Archive for Rational Mechanics and Analysis

, Volume 159, Issue 3, pp 229-252

First online:

An Eulerian Description of Fluids Containing Visco-Elastic Particles

  • Chun LiuAffiliated withDepartment of Mathematics¶Pennsylvania State University¶State College, PA 16802, USA¶e-mail:
  • , Noel J. WalkingtonAffiliated withDepartment of Mathematics¶Carnegie Mellon University¶Pittsburgh, PA 15213, USA¶e-mail:

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Equations governing the flow of fluid containing visco-hyperelastic 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 visco-hyperelastic particles in a Newtonian fluid are established using a Galerkin scheme.