Year: 2016
Communications in Computational Physics, Vol. 20 (2016), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.080615.010216a
Communications in Computational Physics, Vol. 20 (2016), Iss. 4 : pp. 870–901
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32