A novel approach to model the flow of generalized Newtonian fluids with the finite pointset method
Tóm tắt
Several numerical meshless methods have been proposed to try to solve some of the limitations of traditional mesh-based methods. Among those, the finite pointset method, which has been applied in several physical problems, shows a great potential. This work presents an extension of the available numerical approaches based on the finite pointset method to allow dealing with generalized Newtonian fluids, which possess a high viscosity. The developed finite pointset method solver is verified through the comparison of its predictions with analytical solutions, for simple flows, and with results provided by the well-established and validated open-source computational library OpenFOAM, for more complex cases studies. The excellent results obtained on the verification case studies prove the proper implementation of the new finite pointset method solver.
Tài liệu tham khảo
Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: an overview and recent developments. Comput Methods Appl Mech Engrg 139(1–4):3–47
Carneiro OS, Nóbrega JM (2012) Design of extrusion forming tools. Smithers Rapra, London
Chorin AJ (1968) Numerical solution of the Navier–Stokes equations. Math Comput 22(104):745–762
Costa R, Nóbrega JM, Clain S, Machado GJ (2019) Very high-order accurate polygonal mesh finite volume scheme for conjugate heat transfer problems with curved interfaces and imperfect contacts. Comput Methods Appl Mech Eng 357:112560
Fasshauer GE (2006) Meshfree methods. In: Rieth M, Schommers W (eds) Handbook of theoretical and computational nanotechnology, vol 2. American Scientific Publishers, pp 33–97
Gonçalves N, Carneiro O, Nóbrega J (2013) Design of complex profile extrusion dies through numerical modeling. J Non Newtonian Fluid Mech 200:103–110
Gonçalves N, Teixeira P, Ferrás L, Afonso A, Nóbrega J, Carneiro O (2015) Design and optimization of an extrusion die for the production of wood-plastic composite profiles. Polym Eng Sci 55(8):1849–1855
Jasak H, Jemcov A, Tukovic Z et al (2007) Openfoam: A c++ library for complex physics simulations. In: International workshop on coupled methods in numerical dynamics, IUC Dubrovnik Croatia, vol 1000, pp 1–20
Kuhnert J (1999) General smoothed particle hydrodynamics. PhD thesis, Technische Universität Kaiserslautern
Kuhnert J (2003) An upwind finite pointset method (fpm) for compressible Euler and Navier–Stokes equations. In: Meshfree methods for partial differential equations, pp 239–249
Kuhnert J (2014) Meshfree numerical schemes for time dependent problems in fluid and continuum mechanics. In: Advances in PDE modeling and computation, pp 119–136
Kuhnert J, Michel I, Mack R (2017) Fluid structure interaction (FSI) in the meshfree finite pointset method (FPM): theory and applications. In: International workshop on meshfree methods for partial differential equations, pp 73–92
Libreros J, Trujillo M (2021) Effects of mesh generation on modelling aluminium anode baking furnaces. Fluids 6(4):140
Michel I, Seifarth T, Kuhnert J, Suchde P (2021) A meshfree generalized finite difference method for solution mining processes. Comput Part Mech 8(3):561–574
Nguyen VP, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79(3):763–813
Oñate E, Idelsohn S (1998) A mesh-free finite point method for advective-diffusive transport and fluid flow problems. Comput Mech 21(4):283–292
Oñate E, Idelsohn S, Zienkiewicz O, Taylor R (1996) A finite point method in computational mechanics. Applications to convective transport and fluid flow. Int J Numer Methods Eng 39(22):3839–3866
Oñate E, Idelsohn S, Zienkiewicz O, Taylor R, Sacco C (1996) A stabilized finite point method for analysis of fluid mechanics problems. Comput Methods Appl Mech Eng 139(1–4):315–346
Reséndiz-Flores EO, Saucedo-Zendejo FR (2015) Two-dimensional numerical simulation of heat transfer with moving heat source in welding using the finite pointset method. Int J Heat Mass Transf 90:239–245
Reséndiz-Flores EO, Saucedo-Zendejo FR (2018) Meshfree numerical simulation of free surface thermal flows in mould filling processes using the finite pointset method. Int J Therm Sci 127:29–40
Saucedo-Zendejo FR, Reséndiz-Flores EO (2017) A new approach for the numerical simulation of free surface incompressible flows using a meshfree method. Comput Methods Appl Mech Eng 324:619–639
Saucedo-Zendejo FR, Reséndiz-Flores EO (2020) Meshfree numerical approach based on the finite pointset method for static linear elasticity problems. Comput Methods Appl Mech Eng 372:113367
Saucedo-Zendejo FR, Reséndiz-Flores EO, Kuhnert J (2019) Three-dimensional flow prediction in mould filling processes using a GFDM. Comput Part Mech 6(3):411–425
Spanjaards MM, Hulsen MA, Anderson PD (2021) Die shape optimization for extrudate swell using feedback control. J Non Newtonian Fluid Mech 293:104552
Suchde P (2021) A meshfree Lagrangian method for flow on manifolds. Int J Numer Methods Fluids 93(6):1871–1894
Suchde P, Kuhnert J, Tiwari S (2018) On meshfree GFDM solvers for the incompressible Navier–Stokes equations. Comput Fluids 165:1–12
Tiwari S, Kuhnert J (2002) A meshfree method for incompressible fluid flows with incorporated surface tension. Rev Eur Elem 11(7–8):965–987
Tiwari S, Kuhnert J (2007) Modeling of two-phase flows with surface tension by finite pointset method (FPM). J Comput Appl Math 203:376–386
Tomé M, Araujo M, Evans J, McKee S (2019) Numerical solution of the Giesekus model for incompressible free surface flows without solvent viscosity. J Non Newtonian Fluid Mech 263:104–119
Xu R, Stansby P, Laurence D (2009) Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach. J Comput Phys 228(18):6703–6725
Zhang L, Ademiloye A, Liew K (2019) Meshfree and particle methods in biomechanics: prospects and challenges. Arch Comput Methods Eng 26(5):1547–1576