A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes. (2nd August 2017)

• Record Type: Journal Article
• Authors: Niethammer, M.; Marschall, H.; Kunkelmann, C.; Bothe, D.
• Is Part Of: International journal for numerical methods in fluids. Volume 86:Number 2(2018)
• Page Start: 131
• Page End: 166
• Publication Date: 2017-08-02
• Subjects: benchmark results -- finite volume method -- planar contraction -- velocity‐stress‐coupling -- viscoelastic fluid; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4411
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general‐purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full combinatorial flexibility between different kinds of rheological models on the one hand, and effective stabilization methods on the other hand. A special emphasis is put on the velocity‐stress‐coupling on colocated computational grids. Using special face interpolation techniques, a semi‐implicit stress interpolation correction is proposed to correct the cell‐face interpolation of the stress in the divergence operator of the momentum balance. Investigating the entry‐flow problem of the 4:1 contraction benchmark, we demonstrate that the numerical methods are robust over a wide range of Weissenberg numbers and significantly alleviate the high Weissenberg number problem. The accuracy of the results is evaluated in a detailed mesh convergence study. Abstract : A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. The numerical framework provides full combinatorial flexibility between different kinds of rheological models on the one hand, and effective stabilization methods on the other hand. Investigating the entry‐flow problem of the 4:1 contraction benchmark, we demonstrate that the numerical methods are robust over a wide range of Weissenberg numbers and significantly alleviate the high Weissenberg number problem.