Volume 20, Issue 4
Application of the LS-STAG Immersed Boundary/ Cut-Cell Method to Viscoelastic Flow Computations

Olivier Botella, Yoann Cheny, Farhad Nikfarjam & Marcela Stoica

Commun. Comput. Phys., 20 (2016), pp. 870-901.

Published online: 2018-04

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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.

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@Article{CiCP-20-870, author = {}, title = {Application of the LS-STAG Immersed Boundary/ Cut-Cell Method to Viscoelastic Flow Computations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {4}, pages = {870--901}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.080615.010216a}, url = {http://global-sci.org/intro/article_detail/cicp/11176.html} }
TY - JOUR T1 - Application of the LS-STAG Immersed Boundary/ Cut-Cell Method to Viscoelastic Flow Computations JO - Communications in Computational Physics VL - 4 SP - 870 EP - 901 PY - 2018 DA - 2018/04 SN - 20 DO - http://dor.org/10.4208/cicp.080615.010216a UR - https://global-sci.org/intro/article_detail/cicp/11176.html KW - AB -

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.

Olivier Botella, Yoann Cheny, Farhad Nikfarjam & Marcela Stoica. (2020). Application of the LS-STAG Immersed Boundary/ Cut-Cell Method to Viscoelastic Flow Computations. Communications in Computational Physics. 20 (4). 870-901. doi:10.4208/cicp.080615.010216a
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