A staggered projection scheme for viscoelastic flows

O Mokhtari (1, 2) , Yohan Davit (2) , J.-C Latché (3) , Michel Quintard (2)

1 CSTJF - Centre scientifique et Technique Jean Feger
2 IMFT - Institut de mécanique des fluides de Toulouse
3 IRSN - Institut de Radioprotection et de Sûreté Nucléaire

We develop a numerical scheme for the flow of viscoelastic fluids, including the Oldroyd-B and FENE-CR constitutive models. The space discretization is staggered, using either the Marker-And-Cell (MAC) scheme for structured nonuniform grids, or the Rannacher and Turek (RT) nonconforming low-order finite element approximation for general quandrangular or hexahedral meshes. The time discretization uses a fractional-step algorithm where the solution of the Navier-Stokes equations is first obtained by a projection method and then the transport-reaction equation for the conformation tensor is solved by a finite volume scheme. In order to obtain consistency, the space discretization of the divergence of the elastic part of the stress tensor in the momentum balance equation is derived using a weak form of the MAC scheme. For stability and accuracy purposes, the solution of the transport-reaction equation for the conformation tensor is split into pure convection steps, with a change of variable to the log-conformation tensor, and a reaction step, which consists in solving one ODE per cell via an Euler scheme with local sub-cycling. Numerical computations for the flow in the lid-driven cavity at Weissenberg numbers above one and the flow around a confined cylinder confirm the efficiency of the scheme.

Mots clés: viscoelastic flows; finite volume; staggered discretization; projection scheme

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Calcul parallèle, distribué et partagé [cs.DC]

O Mokhtari, Yohan Davit, J.-C Latché, Michel Quintard. A staggered projection scheme for viscoelastic flows. 2021. ⟨hal-03400727⟩