A stabilized hybrid FE/FV method applied to fluid flow in mold filling
Keywords:
casting processes, incompressible flow, pressure stabilization, finite volumes, stabilized finite element methods, MINI elementAbstract
Modern casting processes allow the precise production of parts with complex shapes. Numerical simulation increasingly becomes an important tool aiding design and production. A finite element method using finite volume principles is described. A new adaptive stabilization based either on bubble functions or a Petrov-Galerkin method is elaborated. Then, a new stabilization scheme, named FF-VOF, is presented to describe the free surface evolution during mold filling. Finally, the developed method is applied to the mold filling benchmark defined at the 7th Conference on Modeling of Casting, Welding and Advanced Solidification Processes.
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References
Arnold D. N., Brezzi F., Fortin, M., “A stable finite element for the Stokes equations”,
Calcolo 23, Vol. 4, 1984, pp. 337-334.
Brezzi F., Bristeau M.-O., Franca L. P., Mallet M., Rogé P., “A relationship between
stabilized finite element methods and the Galerkin method with bubble functions”,
Comput. Meth. Appl. Mech. Eng., 1992, pp. 117-129.
Brezzi F., Franca L. P., Hughes T. J. R., Russo A., “Stabilization Techniques and Subgrid
Scale Capturing”, Proceedings of the Conference on the State of the Art in Numerical
Analysis, York, England, IMA Conference Series, Vol. 63 (Duff, I.S. and Watson, G. A.
eds.), Oxford University Press, April 1996, pp. 391-406.
Brezzi F., Franca L. P., Hughes T. J. R., Russo A., “ b = ∫ g ”, Comput. Meth. Appl. Mech.
Eng., Vol. 145, 1997, pp. 329-339.
Brooks A. N., Hughes T. J. R., “SUPG formulations for convection dominated flows with
particular emphasis on the incompressible Navier-Stokes equations”, Comput. Meth.
Appl. Mech. & Eng., Vol. 32, 1982, 199-259.
Cross M., Campbell L., (eds.): Proceedings of Modeling of casting, welding and advanced
solidification, TMS publications, 1995.
Dhatt G., Gao D. M., Ben Cheikh A., “A Finite Element Simulation of Metal Flow in
Moulds”, Int. J. Num. Meth. Eng., 30, 1990, pp. 821-831.
Donea J., “A Taylor-Galerkin Method for Convective Tramsport Problems”, Int. J. Num.
Meth. Eng., 20, 1984, pp. 101-119.
Franca L. P., Frey S. L., Hughes T. J. R., “Stabilized finite element methods: I. Application to
the advective-diffusive model”, Comput. Meth. Appl. Mech. Eng., 95, 1992, pp. 253-276.
Franca L. P., Frey S. L., “Stabilized finite element methods: II. The incompressible Navier-
Stokes equations”, Comput. Meth. Appl. Mech. Eng., 99, 1992, pp. 209-233.
Franca L. P., Russo A., “Deriving Upwinding, Mass Lumping and Selective Reduced
Integration by Residual Free Bubbles”, Appl. Math. Letters, 1996.
Franca L. P., Nesliturk A., Stynes M., “On the stability of residual-free bubbles for
convection-diffusion problems and their approximation by a two-level finite element
method”, Comput. Meth. in Appl. Mech. Eng., 1998, pp. 35-49.
Gresho P. M., Sani B., Incompressible Flow and the Finite Element Method –
Haldenwanger A., Stich A., “Casting Simulation an an Innovation in the Motor Vehicle
Development Process”, in: Proc. of MCWASP - IX, Sahm, P. R., Hansen, P. N., Conley,
J. G. (eds.), Shaker Verlag, pp. XLIV-LI, 2000.
Huerta A., Roig B., Donea J., “Time-Accurate Solution of Convective Transport Problems”,
ECOMAS 2000,
http://www-lacan.upc.es/lacan/articulos/pdf/eccomas2000_huerta_hrd.pdf
Hughes T. J. R., “Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann
formulation, subgrid scale models, bubbles and the origin of stabilized methods”,
Comput. Meth. Appl. Mech. Eng., 127, 1995, pp. 387-401.
Idelsohn S. R., Oñate E., “Finite Volumes and Finite Elements ‘Two good Friends’”, Int. J.
Numer. Meth. Eng., 37, 1994, pp. 3324-3341.
Kothe D. B., Rider W. J., Comments on Modeling Interfacial Flows with Volume-of-Fluid
Methods, http://public.lanl.gov/mww/HomePage.html.
Kothe D. B., Juric D., Lam K., Lally B., Numerical Recipes for Mold Filling Simulation,
http://public.lanl.gov/mww/HomePage.html.
Laschet G., Neises J., Steinbach I., “Micro and Macrosimulation of Casting Processes”, in: 4e
école d´été du GUT, Modélisation numérique en thermique, Lecture Notes, Porquerolles,
Laschet G., Neises J., Diemer M.: “Simulation of Casting Processes with CASTS”, in: 4e
école d´été du GUT, Modélisation numérique en thermique, Workshop, Porquerolles,
Morton K. W., Parrott A. K., “Generalized Galerkin Methods for First Order Hyperbolic
equations”, J. Comp. Phys., 36, 1980, pp. 246-270.
Neises J., Steinbach I., “Finite Element Integration for the Control Volume Method”, Comm.
Num. Meth. Eng., 12, 1996, pp. 543-555.
Neises J., Laschet G., A Fluid Field Method for Transient Free Surfaces, ACCESS, Annual
Report of DFG-CNRS project on numerical free surface flow, 1998.
Neises J., Steinbach I., Delannoy Y., “Modeling of Free Surfaces in Casting Processes”, in:
Notes on Numerical Fluid Mechanics, Vieweg, 1998, pp. 168-186.
Neises J., Stemmler M., Laschet G., “A hybrid Control-Volume Method stabilized by Bubble
Functions applied to Fluid Flow” in Casting Processes, USNCCM99, Book of Abstracts,
, pp. 221.
Neises J., Numerical Modeling of Incompressible Flow Applied to Casting Processes,
PhD thesis, Technical University of Aachen, 2001, http://www.bth.rwth-aachen.de/job/
disslist.pl
Patankar S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere, 1980, Washington
D.C.
Sahm P. R., Hansen P. N., “Towards Integrated Modeling for Intelligent Castings”, in: Proc.
of MCWASP - IX, Shaker Verlag, pp. XLIV-LI, 2000, LXXXI.
Sirrel B., Holliday M., Campbell J., “The benchmark test 1995”, Proc. 7th Int. Conf. on
Modeling of Casting, Welding and Advanced Solidification Processes, TMS 1995,
pp. 915-932.
Song R., Dhatt G., Ben Cheikh A., “Thermo-Mechanical Finite Element Model of Casting
Systems”, Int. J. Num. Meth. in Eng., Vol. 30, 1990, pp. 559-579.
Soulaimani A., Fortin M., Quellet Y., Dhatt G., Bertrand F., “Simple Continuous Pressure
Elements for Two- and Three Dimensional Incompressible Flows”, Comput. Meth. Appl.
Mech. Eng., 62, 1987, pp. 47-69.
Steinbach I., Neises J., “A control volume treatment of finite elements and its application to a
solidification problem”, in Numerical Methods in Thermal Problems, eds. Lewis, R.W. &
Durbetaki P., Vol. IX, 1995, pp. 466-473.
Steinbach I., Ein Multi-Phasen-Feld Modell für facettiertes Kristallwachstum, PhD thesis,
Technical University Aachen, 2000, http://www.bth.rwth-aachen.de/job/disslist.pl.
Tezduyar T. E., Mittal S., Ray S. E., Shih R., “Incompressible flow computations with
stabilized bilinear and linear equal-order-interpolation velocity-pressure elements”,
Comput. Meth. Appl. Mech. Eng., 95, 1992, pp. 221-242.
Zienkiewicz O. C., Onate E., Finite volumes vs. finite elements. Is there really a choice?, in
Nonlinear Computation Mechanics, State of the Art, Wriggers, P. Wagner, W. (eds.),
Springer Verlag, Berlin, 1991.