@Article{CiCP-20-870,
author = {Olivier Botella, Yoann Cheny, Farhad Nikfarjam and Marcela Stoica},
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 = {<p style="text-align: justify;">This paper presents the extension of a well-established Immersed Boundary
(IB)/cut-cell method, the LS-STAG method (Y. Cheny &amp; 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.<br/>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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.080615.010216a},
url = {http://global-sci.org/intro/article_detail/cicp/11176.html}
}