Claude Mangoubi

Numerical Stability of the method of Brownian configuration fields

The computation of viscoelastic flow using macroscopic models is known to be problematic
when the Weissenberg number (the ratio of the typical relaxation time of the
fluid considered to a typical flow time)  reaches a value of O(1).

In the last decade, kinetic (or micro-macro) models have been introduced in the simulation of
viscoelastic fluids. While they seem to have better stability properties than
their macroscopic counterparts, this has not been clearly shown.

In this talk, we investigate the numerical stability of the Brownian configuration fields method
as the Weissenberg (Wi) number increases. We do not encounter the typical numerical
blow-up known in macroscopic models. However, solutions become mesh-dependent as Wi is large.

This lecture is based on joint work with Martien Hulsen and Raz Kupferman.