A free surface finite element model for low Froude number mould filling problems on fixed meshes. (English) Zbl 1452.76084
Summary: The simulation of low Froude number mould filling problems on fixed meshes presents significant difficulties. As the Froude number decreases, the coupling between the position of the interface and the resulting flow field increases. The usual two-phase flow model provides poor results for such flow. In order to overcome the difficulties, a free surface model that applies boundary conditions at the interface accurately is used. Moreover, the use of wall laws on curved boundaries also fails in the case of low Froude number flows. To solve this second problem, we combine wall laws with ’do nothing’ boundary conditions. A special feature of our approach is that ’do nothing’ boundary conditions are only applied in the normal direction. These two key ingredients together with the Level Set method allow us to simulate three-dimensional mould filling problems borrowed directly from the foundry.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76B07 | Free-surface potential flows for incompressible inviscid fluids |
References:
| [1] | Cross, Computational modeling of mold filling sand related free-surface flows in shape casting: an overview of the challenges involved, Metallurgical and Materials Transactions B 37B pp 879– (2006) · doi:10.1007/BF02735009 |
| [2] | Coppola-Owen, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, International Journal for Numerical Methods in Fluids 49 pp 1278– (2005) · Zbl 1080.76036 · doi:10.1002/fld.963 |
| [3] | Coppola-Owen, A finite element model for free surface flows on fixed meshes, International Journal for Numerical Methods in Fluids 54 pp 1151– (2007) · Zbl 1116.76052 · doi:10.1002/fld.1412 |
| [4] | Chang, A level set formulation of Eulerian interface capturing methods, Journal of Computational Physics 124 pp 449– (1996) · Zbl 0847.76048 · doi:10.1006/jcph.1996.0072 |
| [5] | Sussman, An adaptive level set approach for incompressible two phase flows, Journal of Computational Physics 148 pp 81– (1999) · Zbl 0930.76068 · doi:10.1006/jcph.1998.6106 |
| [6] | Osher, Level Set Methods and Dynamic Implicit Surfaces (2003) · doi:10.1007/b98879 |
| [7] | Thompson, Use of the pseudo-concentration to follow creeping viscous during transient analysis, International Journal for Numerical Methods in Engineering 6 pp 749– (1986) · doi:10.1002/fld.1650061005 |
| [8] | Hirt, Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics 39 pp 201– (1981) · Zbl 0462.76020 · doi:10.1016/0021-9991(81)90145-5 |
| [9] | Codina, Mould filling simulation using finite elements, International Journal of Numerical Methods for Heat and Fluid Flow 4 pp 291– (1994) · Zbl 0923.76116 · doi:10.1108/EUM0000000004108 |
| [10] | Lewis, Efficient mould filling simulation in metal castings by an explicit finite element method, International Journal for Numerical Methods in Engineering 20 pp 493– (1995) · Zbl 0845.76046 · doi:10.1002/fld.1650200606 |
| [11] | Codina, A numerical model to track two-fluid interfaces based on a stabilized finite element method sand the level set technique, International Journal for Numerical Methods in Fluids 40 pp 293– (2002) · Zbl 1010.76053 · doi:10.1002/fld.277 |
| [12] | Ramaswamy, Numerical simulation of unsteady viscous free surface flow, Journal of Computational Physics 90 pp 396– (1990) · Zbl 0701.76036 · doi:10.1016/0021-9991(90)90173-X |
| [13] | Ramaswamy, Lagrangian finite element method for the analysis of two-dimensional sloshing problems, International Journal for Numerical Methods in Fluids 6 pp 659– (1985) · Zbl 0597.76026 · doi:10.1002/fld.1650060907 |
| [14] | Radovitzky, Lagrangian finite element analysis of Newtonian fluid flows, Journal of Computational Physics 43 pp 607– (1998) · Zbl 0945.76047 |
| [15] | Launder, The numerical computation of turbulent flows, Computer Methods in Applied Mechanics and Engineering 3 pp 269– (1974) · Zbl 0277.76049 · doi:10.1016/0045-7825(74)90029-2 |
| [16] | Behr, On the application of slip boundary conditions on curved boundaries, International Journal for Numerical Methods in Fluids 45 pp 43– (2004) · Zbl 1079.76576 · doi:10.1002/fld.663 |
| [17] | Pichelin, Finite element solution of the 3D mold filling problem for viscous incompressible fluid, Computer Methods in Applied Mechanics and Engineering 163 pp 359– (1998) · Zbl 0963.76051 · doi:10.1016/S0045-7825(98)00024-3 |
| [18] | Hartmann, Differential equation based constrained reinitialization for level set methods, Journal of Computational Physics 227 pp 6821– (2007) · Zbl 1189.76366 · doi:10.1016/j.jcp.2008.03.040 |
| [19] | Garcia-Espinosa, ODDLS: a new unstructured mesh finite element method for the analysis of free surface flow problems, International Journal for Numerical Methods in Engineering 76 pp 1297– (2008) · Zbl 1195.76253 · doi:10.1002/nme.2348 |
| [20] | Löhner, On the simulation of flows with violent free surface motion, Computer Methods in Applied Mechanics and Engineering 195 pp 5597– (2006) · Zbl 1122.76070 · doi:10.1016/j.cma.2005.11.010 |
| [21] | Houzeaux, A finite element model for the simulation of lost foam casting, International Journal for Numerical Methods in Fluids 46 pp 203– (2004) · Zbl 1060.76572 · doi:10.1002/fld.757 |
| [22] | Codina, The fixed-mesh ALE approach for the numerical approximation of flows in moving domains, Journal of Computational Physics 228 pp 1591– (2009) · Zbl 1409.76100 · doi:10.1016/j.jcp.2008.11.004 |
| [23] | Codina, Stabilized finite element approximation of transient incompressible flows using orthogonal subscales, Computer Methods in Applied Mechanics and Engineering 191 pp 4295– (2002) · Zbl 1015.76045 · doi:10.1016/S0045-7825(02)00337-7 |
| [24] | Codina, Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales, Applied Numerical Mathematics 58 pp 264– (2008) · Zbl 1144.76029 · doi:10.1016/j.apnum.2006.11.011 |
| [25] | Brezzi, Mixed and Hybrid Finite Element Methods (1991) · Zbl 0788.73002 · doi:10.1007/978-1-4612-3172-1 |
| [26] | Gresho, Incompressible Flow and the Finite Element Method (2000) · Zbl 0988.76005 |
| [27] | Papanastasiou, A new outflow boundary condition, International Journal for Numerical Methods in Fluids 14 pp 587– (1992) · Zbl 0747.76039 · doi:10.1002/fld.1650140506 |
| [28] | Caboussat, Numerical simulation of two-phase free surface flows, Archives of Computational Methods in Engineering 12 pp 165– (2005) · Zbl 1097.76047 · doi:10.1007/BF03044518 |
| [29] | Gao, A three dimensional finite element-volume tracking model for mould filling in casting processes, International Journal for Numerical Methods in Fluids 29 pp 877– (1999) · Zbl 0953.76046 · doi:10.1002/(SICI)1097-0363(19990415)29:7<877::AID-FLD814>3.0.CO;2-7 |
| [30] | Saad, Iterative Methods for Sparse Linear Systems (1996) · Zbl 1031.65047 |
| [31] | Elias, Stabilized edge-based finite element simulation of free-surface flows, International Journal for Numerical Methods in Fluids 54 pp 965– (2007) · Zbl 1258.76111 · doi:10.1002/fld.1475 |
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