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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2023

A staggered projection scheme for viscoelastic flows

Résumé

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 quadrangular 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.
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Origine : Publication financée par une institution
Licence : CC BY - Paternité
Origine : Publication financée par une institution
Licence : CC BY - Paternité

Dates et versions

irsn-04388582 , version 1 (11-01-2024)

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Paternité

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Omar Mokhtari, Yohan Davit, Jean Claude Latche, Michel Quintard. A staggered projection scheme for viscoelastic flows. ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57 (3), pp.1747-1793. ⟨10.1051/m2an/2023020⟩. ⟨irsn-04388582⟩
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