Abstract:
A numerical model is presented for the simulation of viscoelastic flows
(Oldroyd-B)
with complex free surfaces in three space dimensions.
The mathematical formulation of the model is similar to that of the volume
of fluid (VOF)
method, but the numerical procedures are different.
The time discretization is based on a splitting scheme.
The first step consists in solving advection equations whilst the second
step corresponds to
a simplified Oldroyd-B problem in a fixed domain.
Numerical results will be presented for the buckling of a jet and for the
stretching of a filament.
Extension to the stochastic Hookean dumbbells model is then discussed and a finite element discretization in space is proposed. Existence of the numerical solution is proved for small data, as well as a priori error estimates, using an implicit function theorem framework.
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