A numerical methodology for simulation of non-Newtonian viscoelastic flows

References

• D. M. Binding , P. M. Phillips and T. N. Phillips , “Contraction/expansion flows: the pressure drop and related issues,” J. Non-Newtonian Fluid Mech. , vol. 137, no. 1-3, pp. 31–38, 2006. DOI: 10.1016/j.jnnfm.2006.03.006.
   Web of Science ®Google Scholar
• R. G. Sousa et al. , “Lid-driven cavity flow of viscoelastic liquids,” J. Non-Newtonian Fluid Mech. , vol. 234, pp. 129–138, 2016. DOI: 10.1016/j.jnnfm.2016.03.001.
   Web of Science ®Google Scholar
• A. Shahbani-Zahiri , H. Hassanzadeh , M. M. Shahmardan and M. Norouzi , “Investigation of Pitchfork bifurcation phenomena effects on heat transfer of viscoelastic flow inside a symmetric sudden expansion,” Phys. Fluids , vol. 29, no. 11, pp. 113101:1–16, 2017. DOI: 10.1063/1.5009434.
   Web of Science ®Google Scholar
• R. J. Poole , F. T. Pinho , M. A. Alves and P. J. Oliveira , “the effect of expansion ratio for creeping expansion flows of UCM fluids,” J. Non-Newtonian Fluid Mech. , vol. 163, no. 1–3, pp. 35–44, 2009. DOI: 10.1016/j.jnnfm.2009.06.004.
   Web of Science ®Google Scholar
• M. A. Alves , P. J. Oliveira and F. T. Pinho , “A convergent and universally bounded interpolation scheme for the treatment of advection,” Int. J. Numer. Methods Fluids , vol. 41, no. 1, pp. 47–75, 2003. DOI: 10.1002/fld.428.
   Web of Science ®Google Scholar
• A. Wachs , J. R. Clermont and A. Khalifeh , “Computations of non-isothermal viscous and viscoelastic flows in abrupt contractions using finite volume method,” Eng. Comput. , vol. 19, no. 8, pp. 874–901, 2002. DOI: 10.1108/02644400210450332.
   Google Scholar
• P. S. B. Zdanski , M. A. Ortega and N. G. C. R. Fico, Jr. , “Numerical simulation of the incompressible Navier-Stokes equations,” Numer. Heat Transfer B , vol. 46, no. 6, pp. 549–579, 2004. DOI: 10.1080/104077990503663.
   Web of Science ®Google Scholar
• M. Vaz, Jr. , and P. S. B. Zdanski , “A fully implicit finite difference scheme for velocity and temperature coupled solutions of polymer melt flow,” Commun. Numer. Methods Eng. , vol. 23, no. 4, pp. 285–294, 2006. DOI: 10.1002/cnm.902.
   Google Scholar
• P. S. B. Zdanski , M. Vaz, Jr. , and G. R. Inácio , “A finite volume approach to simulation of polymer melt flow in channels,” Eng. Comput. , vol. 25, no. 3, pp. 233–250, 2008. DOI: 10.1108/02644400810857074.
   Google Scholar
• P. S. B. Zdanski and M. Vaz, Jr. , “A numerical method for simulation of incompressible three-dimensional Newtonian and non-Newtonian flows,” Numer. Heat Transfer B , vol. 59, no. 5, pp. 360–380, 2011. DOI: 10.1080/10407790.2011.572727.
   Web of Science ®Google Scholar
• P. Tamamidis , G. Zhang and D. N. Assanis , “Comparison of pressure-based and artificial compressibility methods for solving 3D steady incompressible viscous flows,” J. Comput. Phys. , vol. 124, no. 1, pp. 1–13, 1996. DOI: 10.1006/jcph.1996.0041.
   Web of Science ®Google Scholar
• A. J. Chorin , “A numerical method for solving incompressible viscous flows problems,” J. Comput. Phys. , vol. 2, no. 1, pp. 12–26, 1967. DOI: 10.1016/0021-9991(67)90037-X.
   Google Scholar
• F. H. Harlow and J. E. Welch , “Numerical calculation of time-dependent viscous incompressible flow of fluid with free-surface,” Phys. Fluids , vol. 8, no. 12, pp. 2182–2189, 1965. DOI: 10.1063/1.1761178.
   Web of Science ®Google Scholar
• S. V. Patankar and D. B. Spalding , “A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows,” Int. J. Heat Mass Transfer , vol. 15, no. 10, pp. 1787–1806, 1972. DOI: 10.1016/0017-9310(72)90054-3.
   Web of Science ®Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow . Washington, DC: Hemisphere Publishing Corporation, pp. 113–137, 1980.
   Google Scholar
• J. P. Van Doormaal and G. D. Raithby , “Enhancements of the SIMPLE method for predicting incompressible fluid flow,” Num. Heat Transfer B Fundam. , vol. 7, no. 2, pp. 147–163, 1984. DOI: 10.1080/10407798408546946.
   Web of Science ®Google Scholar
• C. R. Maliska , “A Solution Method for Three-Dimensional Parabolic Fluid Flow Problems in Non-orthogonal Coordinates,” PhD. thesis, University of Waterloo, Waterloo, 1981.
   Google Scholar
• Z. G. Qu , W. Q. Tao and Y. L. He , “An improved numerical scheme for the SIMPLER method on non-orthogonal curvilinear coordinates: SIMPLERM,” Numer. Heat Transfer B , vol. 51, no. 1, pp. 43–66, 2007. DOI: 10.1080/10407790600682797.
   Web of Science ®Google Scholar
• A. Dalal , V. Eswaran and G. Biswas , “A finite-volume method for Navier-Stokes equations on unstructured meshes,” Numer. Heat Transfer B , vol. 54, no. 3, pp. 238–259, 2008. DOI: 10.1080/10407790802182653.
   Web of Science ®Google Scholar
• G. R. Inácio , J. C. Tomio , M. Vaz, Jr , and P. S. B. Zdanski , “Numerical study of viscoplastic flow in a T-bifurcation: identification of stagnant regions,” Braz. J. Chem. Eng. , vol. 36, no. 3, pp. 1279–1287, 2019. DOI: 10.1590/0104-6632.20190363s20180361.
   Web of Science ®Google Scholar
• S. Ingelsten , A. Mark , K. Jareteg , R. Kádár and F. Edelvik , “Computationally efficient viscoelastic flow simulation using a Lagrangian-Eulerian method and GPU-acceleration,” J. Non-Newtonian Fluid Mech. , vol. 279, pp. 104264, 2020. DOI: 10.1016/j.jnnfm.2020.104264.
   Web of Science ®Google Scholar
• J. G. Oldroyd , “On the formulation of rheological equations of state,” Proc. R. Soc. Lond. A , vol. 200, no. 1063, pp. 523–541, 1950.
   Web of Science ®Google Scholar
• D. Rajagopalan , R. C. Armstrong and R. A. Brown , “Finite element methods for calculation of steady, viscoelastic flow using constitutive equations with a Newtonian viscosity,” J. Non-Newtonian Fluid Mech. , vol. 36, pp. 159–192, 1990. DOI: 10.1016/0377-0257(90)85008-M.
   Web of Science ®Google Scholar
• R. M. Beam and R. F. Warming , “An implicit factored scheme for the compressible Navier-Stokes equations,” AIAA J. , vol. 16, no. 4, pp. 393–402, 1978. DOI: 10.2514/3.60901.
   Google Scholar
• M. F. Tomé , N. Mangiavacchi , J. A. Cuminato , A. Castelo and S. McKee , “A finite difference technique for simulating unsteady viscoelastic free surface flows,” J. Non-Newtonian Fluid Mech. , vol. 106, no. 2-3, pp. 61–106, 2002. DOI: 10.1016/S0377-0257(02)00064-2.
   Web of Science ®Google Scholar
• O. C. Zienkiewicz and R. L. Taylor , The Finite Element Method , vol. 1, 5th ed. London: Butterworth-Heinemann, 2000.
   Google Scholar
• O. Botella , “On the solution of the Navier-Stokes equations using Chebyshev projection schemes with third-order accuracy in time,” Comput. Fluids , vol. 26, no. 2, pp. 107–116, 1997. DOI: 10.1016/S0045-7930(96)00032-1.
   Web of Science ®Google Scholar
• T. W. Pan , J. Hao and R. Glowinski , “On the simulation of a time-dependent cavity flow of an Oldroyd-B fluid,” Int. J. Numer. Methods Fluids , vol. 60, no. 7, pp. 791–808, 2009. DOI: 10.1002/fld.1919.
   Web of Science ®Google Scholar
• C. R. Garibotti , “Uma metodologia de volumes finitos para a resolução de escoamentos viscoelásticos com malhas não-estruturadas híbridas,” Ph.D. thesis, Dept. of Mechanical Engineering, Federal Univ. of Santa Catarina, Florianópolis, SC/Brazil, 2014.
   Google Scholar