Application of the LS-STAG Immersed Boundary/ Cut-Cell Method to Viscoelastic Flow Computations (Communications in Computational Physics, 2018)
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-volumemethod 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 conservationproperties equations be satisfied at the discrete level, resulting in a stable andaccurate method and, thanks to the level-set representation of the IB boundary, at lowcomputational costs.In the present work, we consider a general viscoelastic tensorial equation whose particularcases recover well-known constitutive laws such as the Oldroyd-B, White-Metznerand Giesekus models. Based on the LS-STAG discretization of the Newtonian stressesin the cut-cells, we have achieved a compatible velocity-pressure-stress discretizationthat prevents spurious oscillations of the stress tensor. Applications to popular benchmarksfor viscoelastic fluids are presented: the four-to-one abrupt planar contractionflows with sharp and rounded re-entrant corners, for which experimental and numericalresults are available. The results show that the LS-STAG method demonstrates anaccuracy and robustness comparable to body-fitted methods.