Stationary Oldroyd model with diffusive stress in thin pipes

Laurent Chupin (1) , Andrei Ichim (1) , Sébastien Martin (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

The aim of this paper is to study the stationary flow of an Oldroyd fluid with particular diffusive stress, flowing through a thin 3D pipe. An asymptotic expansion with respect to a small parameter describing the ratio between the diameter of the cross section and the length is calculated and rigorously justified. The result obtained is compared against a numerical solution in the particular case of axisymmetric geometries.

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]

Laurent Chupin, Andrei Ichim, Sébastien Martin. Stationary Oldroyd model with diffusive stress in thin pipes. 2017. ⟨hal-01456091⟩