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Application of the LS-STAG Immersed Boundary/Cut-Cell Method to Viscoelastic Flow Computations

Part of: Basic methods in fluid mechanics Foundations, constitutive equations, rheology Incompressible viscous fluids

Published online by Cambridge University Press:  05 October 2016

Olivier Botella ,
Yoann Cheny ,
Farhad Nikfarjam  and
Marcela Stoica
Olivier Botella*
Affiliation:
LEMTA, Université de Lorraine, CNRS, 2 avenue de la Forêt de Haye – TSA 60604, 54518 Vandoeuvre Cedex, France
Yoann Cheny*
Affiliation:
LEMTA, Université de Lorraine, CNRS, 2 avenue de la Forêt de Haye – TSA 60604, 54518 Vandoeuvre Cedex, France
Farhad Nikfarjam
Affiliation:
LEMTA, Université de Lorraine, CNRS, 2 avenue de la Forêt de Haye – TSA 60604, 54518 Vandoeuvre Cedex, France
Marcela Stoica
Affiliation:
LEMTA, Université de Lorraine, CNRS, 2 avenue de la Forêt de Haye – TSA 60604, 54518 Vandoeuvre Cedex, France
*
*Corresponding author. Email addresses:olivier.botella@univ-lorraine.fr (O. Botella), yoann.cheny@univ-lorraine.fr (Y. Cheny)
*Corresponding author. Email addresses:olivier.botella@univ-lorraine.fr (O. Botella), yoann.cheny@univ-lorraine.fr (Y. Cheny)
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Abstract

This paper presents the extension of a well-established Immersed Boundary (IB)/cut-cell method, the LS-STAG method (Y. Cheny & O. Botella, J. Comput. Phys. Vol. 229, 1043-1076, 2010), to viscoelastic flow computations in complex geometries. We recall that for Newtonian flows, the LS-STAG method is based on the finite-volume method on staggered grids, where the IB boundary is represented by its level-set function. The discretization in the cut-cells is achieved by requiring that global conservation properties equations be satisfied at the discrete level, resulting in a stable and accurate method and, thanks to the level-set representation of the IB boundary, at low computational costs.

In the present work, we consider a general viscoelastic tensorial equation whose particular cases recover well-known constitutive laws such as the Oldroyd-B, White-Metzner and Giesekus models. Based on the LS-STAG discretization of the Newtonian stresses in the cut-cells, we have achieved a compatible velocity-pressure-stress discretization that prevents spurious oscillations of the stress tensor. Applications to popular benchmarks for viscoelastic fluids are presented: the four-to-one abrupt planar contraction flows with sharp and rounded re-entrant corners, for which experimental and numerical results are available. The results show that the LS-STAG method demonstrates an accuracy and robustness comparable to body-fitted methods.

Keywords

Immersed boundary methodcut-cell methodincompressible flowsviscoelastic fluidsplanar contraction flows

MSC classification

Secondary: 68U20: Simulation 76A10: Viscoelastic fluids 76D05: Navier-Stokes equations 76M12: Finite volume methods 76M25: Other numerical methods
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 4 , October 2016 , pp. 870 - 901
Copyright
Copyright © Global-Science Press 2016 

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