Testing viscoelastic numerical schemes using the Oldroyd-B fluid in Newtonian kinematics

Author(s)

Evans, J. D. ; Franca, H. L. ; Palhares Junior, I. L. ; Oishi, C. M.

• Document type: Journal article
• Source: Applied Mathematics and Computation; v. 387, p. 32-pg., 2020-12-15.

Abstract

We focus here on using a Newtonian velocity field to evaluate numerical schemes for two different formulations of viscoelastic flow. The two distinct formulations we consider, correspond to either using a fixed basis for the elastic stress or one that uses the flow directions or streamlines. The former is the traditional Cartesian stress formulation, whilst the later may be referred to as the natural stress formulation of the equations. We choose the Oldroyd-B fluid and three benchmarks in computational rheology: the 4:1 contraction flow, the stick-slip and cross-slot problems. In the context of the contraction flow, fixing the kinematics as Newtonian, actually gives a larger stress singularity at the re-entrant corner, the matched asymptotics of which are presented here. Numerical results for temporal and spatial convergence of the two formulations are compared first in this decoupled velocity and elastic stress situation, to assess the performance of the two approaches. This may be regarded as an intermediate test case before proceeding to the far more difficult fully coupled velocity and stress situation. We also present comparison results between numerics and asymptotics for the stick-slip problem. Finally, the natural stress formulation is used to investigate the cross-slot problem, again in a Newtonian velocity field. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 16/20389-8 - Numerical study of the natural stress formulation for free surface problems
• Grantee: Irineu Lopes Palhares Junior
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 18/22242-0 - Free surface flows of complex fluids
• Grantee: Murilo Francisco Tome
• 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
• FAPESP's process: 14/17348-2 - Stability of Numerical methods for Viscoelastic high Weissenberg number flows
• Grantee: Irineu Lopes Palhares Junior
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 19/01811-9 - Numerical simulation of free surface complex flows
• Grantee: Hugo Leonardo França
• Support Opportunities: Scholarships in Brazil - Doctorate