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A Marker-and-Cell scheme for viscoelastic flows on nonuniform grids

Mokhtari, Omar and Davit, Yohan and Latché, Jean-Claude and de Loubens, Romain and Quintard, Michel A Marker-and-Cell scheme for viscoelastic flows on nonuniform grids. (2020) In: FVCA 2020: Finite Volumes for Complex Applications IX, 15 June 2020 - 19 June 2020 (Bergen, Norway).

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Official URL: https://doi.org/10.1007/978-3-030-43651-3_61

Abstract

In this paper, we develop a numerical scheme for the solution of the coupled Stokes and Navier-Stokes equations with constitutive equations describing the flow of viscoelastic fluids. The space discretization is based on the so-called Marker-And-Cell (MAC) scheme. 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 reasons, the solution of the transport-reaction equation for the conformation tensor is split into pure convection steps, with a change of variable from c to log(c), and a reaction step, which consists in solving one ODE per cell via an Euler scheme with local sub-cycling. Numerical computations for the Stokes flow of an Oldroyd-B fluid in the lid-driven cavity at We=1 confirm the scheme efficiency.

Item Type:Conference or Workshop Item (Paper)
HAL Id:hal-02950581
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
French research institutions > Institut de Radioprotection et de Sûreté Nucléaire - IRSN (FRANCE)
Other partners > Total (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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Deposited On:28 Sep 2020 08:25

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