A modified effective capacitance method for solidification modelling using linear tetrahedral finite elements. (English) Zbl 0879.76045
The main feature of the new method is that a modified form of effective heat capacitance is calculated from the solution of nonlinear equations that describe the energy loss for linear tetrahedral finite elements. This approach ensures that the predicted temperature field corresponds exactly with the energy loss so providing an extremely stable formulation. The method is tested against a range of problems including some with nonlinear liquid fractions.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76T99 | Multiphase and multicomponent flows |
| 80A22 | Stefan problems, phase changes, etc. |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
References:
| [1] | Free and Moving Boundary Problems, Clarendon Press, Oxford, 1984. |
| [2] | Voller, Int. J. Heat Mass Transfer 24 pp 545– (1980) |
| [3] | Voller, Int. J. Heat Mass Transfer 30 pp 147– (1983) |
| [4] | Voller, Numer. Heat Transfer B 17 pp 155– (1990) |
| [5] | Tamma, Int. J. numer. methods eng. 30 pp 803– (1990) |
| [6] | Lewis, Appl. Sci. Res. 44 pp 61– (1987) |
| [7] | Bushko, Numer. Heat Transfer B 19 pp 31– (1991) |
| [8] | Runnels, Numer. Heat Transfer B 19 pp 13– (1991) |
| [9] | Rolph, Int. j. numer. methods eng. 20 pp 217– (1984) |
| [10] | Roose, Int. J. numer. methods eng. 20 pp 217– (1984) |
| [11] | Chen, Int. J. Machine Tools Manufacture 31 pp 1– (1991) |
| [12] | Voller, Int. j. numer. methods eng. 30 pp 875– (1990) |
| [13] | Dalhuijsen, Int. J. numer. methods eng. 23 pp 1807– (1986) |
| [14] | Salcudean, Int. J. numer. methods eng. 25 pp 445– (1988) |
| [15] | and , Fundamentals of Solidification, Trans-Tech., Switzerland, 1986. |
| [16] | and , The Finite Element Method, McGraw-Hill, New York, 1989. |
| [17] | and , Matrix Computations, 2nd edn, The John Hopkins University Press, London, 1991. |
| [18] | Voller, Appl. Math. Modelling 13 pp 3– (1989) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
