A finite difference technique for solving a time strain separable K-BKZ constitutive equation for two-dimensional moving free surface flows

Autor(es)

Tome, M. F. ^[1] ; Bertoco, J. ^[1] ; Oishi, C. M. ^[2] ; Araujo, M. S. B. ^[3] ; Cruz, D. ^[4] ; Pinho, F. T. ^[5] ; Vynnycky, M. ^[6]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Matemat Aplicada & Estat, Ave Trabalhador Sao Carlense, 400 Ctr, Sao Carlos, SP - Brazil

^[2] Univ Estadual Paulista, Dept Matemat & Comp, Rua Roberto Simonsen 305, BR-19060900 Presidente Prudente - Brazil

^[3] Fed Univ Para, Fac Matemat, BR-66059 Belem, Para - Brazil

^[4] Univ Fed Rio de Janeiro, Dept Engn Mecan, Rio De Janeiro - Brazil

^[5] Univ Porto, Dept Engn Mecan, Fac Engn, Ctr Estudos Fenomenos Transporte, Rua Dr Roberto Frias S-N, P-4200465 Oporto - Portugal

^[6] Royal Inst Technol, Dept Mat Sci & Engn, Brinellvagen 23, S-10044 Stockholm - Sweden

• Tipo de documento: Artigo Científico
• Fonte: Journal of Computational Physics; v. 311, p. 114-141, APR 15 2016.
• Citações Web of Science: 9

Resumo

This work is concerned with the numerical solution of the K-BKZ integral constitutive equation for two-dimensional time-dependent free surface flows. The numerical method proposed herein is a finite difference technique for simulating flows possessing moving surfaces that can interact with solid walls. The main characteristics of the methodology employed are: the momentum and mass conservation equations are solved by an implicit method; the pressure boundary condition on the free surface is implicitly coupled with the Poisson equation for obtaining the pressure field from mass conservation; a novel scheme for defining the past times t' is employed; the Finger tensor is calculated by the deformation fields method and is advanced in time by a second-order Runge-Kutta method. This new technique is verified by solving shear and uniaxial elongational flows. Furthermore, an analytic solution for fully developed channel flow is obtained that is employed in the verification and assessment of convergence with mesh refinement of the numerical solution. For free surface flows, the assessment of convergence with mesh refinement relies on a jet impinging on a rigid surface and a comparison of the simulation of a extrudate swell problem studied by Mitsoulis (2010) {[}44] was performed. Finally, the new code is used to investigate in detail the jet buckling phenomenon of K-BKZ fluids. (C) 2016 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 11/13930-0 - Desenvolvimento de um método numérico para simular escoamentos transientes viscoelásticos com superfícies livres
• Beneficiário: Gilcilene Sanchez de Paulo
• Modalidade de apoio: Auxílio à Pesquisa - Regular