Application of the LS-STAG Immersed Boundary/Cut-Cell Method to Viscoelastic Flow Computations. (5th October 2016)

• Record Type: Journal Article
• Authors: Botella, Olivier; Cheny, Yoann; Nikfarjam, Farhad; Stoica, Marcela
• Is Part Of: Communications in computational physics. Volume 20:Number 4(2016:Oct.)
• Page Start: 870
• Page End: 901
• Publication Date: 2016-10-05
• Subjects: 68U20, -- 76A10, -- 76D05, -- 76M12, -- 76M25; Immersed boundary method, -- cut-cell method, -- incompressible flows, -- viscoelastic fluids, -- planar contraction flows; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.080615.010216a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.