Transient computations using the natural stress formulation for solving sharp corner flows

Author(s)

Evans, J. D. ^[1] ; Oishi, C. M. ^[2]

Affiliation

^[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon - England

^[2] Univ Estadual Paulista, Dept Matemat & Computacao, Fac Ciencias & Tecnol, BR-19060900 Presidente Prudente, SP - Brazil

• Document type: Journal article
• Source: Journal of Non-Newtonian Fluid Mechanics; v. 249, p. 48-52, NOV 2017.
• Web of Science Citations: 2

Abstract

In this short communication, we analyse the potential of the natural stress formulation (NSF) (i.e. aligning the stress basis along streamlines) for computing planar flows of an Oldroyd-B fluid around sharp corners. This is the first attempt to combine the NSF into a numerical strategy for solving a transient fluid flow problem considering the momentum equation in Navier-Stokes form (the elastic stress entering as a source term) and using the constitutive equations for natural stress variables. Preliminary results of the NSF are motivating in the sense that accuracy of the numerical solution for the extra stress tensor is improved near to the sharp corner. Comparison studies among the NSF and the Cartesian stress formulation (CSF) (i.e. using a fixed Cartesian stress basis) are conducted in a typical benchmark viscoelastic fluid flow involving a sharp corner: the 4 : 1 contraction. The CSF needs a mesh approximately 10 times smaller to capture similar near singularity results to the NSF. (C) 2017 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 15/50094-7 - Asymptotics and simulation of complex fluids
• Grantee: José Alberto Cuminato
• Support Opportunities: Regular Research Grants
• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC