Modeling Viscoelastic Flows Using Reflected Stochastic Differential Equations

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 Ito 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.