Communications in Mathematical Sciences

Volume 8 (2010)

Number 3

Special Issue: Mathematical Issues of Complex Fluids

Modeling viscoelastic flows using reflected stochastic differential equations

Pages: 655 – 670

DOI: http://dx.doi.org/10.4310/CMS.2010.v8.n3.a3

Authors

A. Bonito

A. Lozinski

T. Mountford

Abstract

A reflected diffusion process is proposed for modeling of viscoelastic fluids. In order to define the viscoelastic stress tensor, the reflected diffusion process is approximated by Itô diffusions with a penalization factor in the drift term. Convergence of the stress tensor approximation is proved and an expression for the limiting stress tensor in terms of the reflected process itself is provided.

Keywords

Viscoelastic flows; dumbbell models; reflected stochastic; differential equations

2010 Mathematics Subject Classification

60H10, 60H35, 76A05

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