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A staggered projection scheme for viscoelastic flows

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-03400727
Contributor : Yohan Davit Connect in order to contact the contributor
Submitted on : Monday, October 25, 2021 - 10:28:36 AM
Last modification on : Wednesday, October 27, 2021 - 2:58:02 PM
Long-term archiving on: : Wednesday, January 26, 2022 - 6:56:23 PM

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  • HAL Id : hal-03400727, version 1

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

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