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An enthalpy formulation based on an arbitrarily deforming mesh for solution of the Stefan problem

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Abstract

Traditionally schemes for dealing with the Stefan phase change problem are separated into fixed grif or front tracking (deforming grid) schemes. A standard fixed grid scheme is to use an enthalpy formulation and track the movement of the phase front via a liquid fraction variable. In this paper, an enthalpy formulation is applied on a continuously deforming finite element grid. This approach results in a general numerical scheme that incorporates both front tracking and fixed grid schemes. It is shown how on appropriate setting of the grid velocity a fixed or deforming grid solution can be generated from the general scheme. In addition an approximate front tracking scheme is developed which can produce accurate non-oscillatory predictions at a computational cost close to an efficient fixed grid scheme. The versatility of the general scheme and the approximate front tracking scheme are demonstrated on solution of a number of Stefan problems in both one and two dimensions.

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References

  • Bell, G. E. 1982: On the enthalpy method. Int. J. Heat Mass Transfer 25: 587–589

    Google Scholar 

  • Bonnerot, R.; Jamet, P. 1977: Numerical computational of the free boundary for the two dimensional Stefan problem by space-time finite elements. J. Comput. Phys. 32: 145–167

    Google Scholar 

  • Crank, J. 1984: Free and moving boundary problems. Oxford: Claredon Press

    Google Scholar 

  • Demirdzic, I.; Peric, M. 1990: Finite volume methods for prediction of fluid flow in arbitrary shaped domains with moving boundaries. Int. J. Num. Mech. Fluids 10: 771–790

    Google Scholar 

  • Fabbri, M.; Voller, V. R. 1993: Numerical solution of plane front solidification with kinetic undercooling. Submitted to Numerical Heat Transfer B

  • Ghosh, S.; Moorthy, S. 1992: An arbitrary Lagrangian-Eulerian element analysis of solidification problems. In: Chenot, J. L.; Wood, R. D.; Zienkiewicz, O. C. (eds.), Numerical methods in industrial forming processes pp. 809–810. Rotterdam: A. A. Balkema

    Google Scholar 

  • Griffith, R.; Nassersharif, B. 1990: Comparison of one-dimensional interface-following and enthalpy methods for the numerical solution of phase changes. Numerical Heat Transfer, Part B 18: 167–187

    Google Scholar 

  • Lacroix, M. 1989. Computation of heat transfer during melting of a pure substance from an isothermal wall. Numerical Heat Transfer, Part B 15: 191–210

    Google Scholar 

  • Lacroix, M; Voller, V. R. 1990. Finite difference solutions of solidification phase change problems: Transformed versus fixed grids. Numerical Heat Transfer, Part B 17: 25–42

    Google Scholar 

  • Li, C. H. 1983 A finite-element front tracking enthalpy method for Stefan problems. IMA J. Numerical Analysis 3: 87–107

    Google Scholar 

  • Lynch, D. R.; O'Neill, K. 1981: Continuously deforming finite elements for solution of parabolic problems with and without phase change. Int. J. Num. Meth. Eng. 17: 81–96

    Google Scholar 

  • Lynch, D. R. 1982: Unified approach to simulation on deforming elements with application to phase change problems. J. Comput. Phys. 47: 387–411

    Google Scholar 

  • Price, P. H.; Slack, M. R. 1954: The effect of latent heat on numerical solutions of the heat flow equation. Brit. J. Appl. Phys. 5: 285–287

    Google Scholar 

  • Schneider, G. E. 1988: Elliptic systems: Finite-element method I. In: Minkowycz, W. J.; Sparrow, E. M.; Schneider, G. E.; Pletcher, R. H. (eds.) Handbook of Numerical Heat Transfer, pp. 379–420. New York: John Wiley

    Google Scholar 

  • Swaminathan, C. R.; Voller, V. R. 1993: On the enthalpy method. Int J. Num. Meth. Heat Fluid Flow 3: 233–244

    Google Scholar 

  • Viswanath, R.; Jaluria, Y. 1993: A comparison of different solution methodologies for melting and solidification problems in enclosures. Numerical Heat Transfer 24: 77–105

    Google Scholar 

  • Voller, V. R.; Cross, M. 1981: Accurate solutions of moving boundary problems using the enthalpy method. Int. J. Heat Mass Transfer 24: 545–556

    Google Scholar 

  • Voller, V. R.; Swaminathan, C. R. 1991: General source based method for solidification phase change. Numerical Heat Transfer, Part B 19: 175–190

    Google Scholar 

  • Voller, V. R.; Swaminathan, C. R. 1993: Treatment of discontinuous thermal conductivity in control volume solutions of phase change problems. Numerical Heat Transfer, Part B (in press)

  • Voller, V. R.; Swaminathan, C. R.; Thomas, B. G. 1990: Fixed grid techniques for phase change problems: a review. Int. J. Num. Meth. Eng. 30: 875–898

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil and Mineral Engineering, University of Minnesota, Minneapolis, Min., USA

    V. R. Voller & S. Peng

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  1. V. R. Voller
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  2. S. Peng
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Communicated by Y. Jaluria, 28 February 1994

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Voller, V.R., Peng, S. An enthalpy formulation based on an arbitrarily deforming mesh for solution of the Stefan problem. Computational Mechanics 14, 492–502 (1994). https://doi.org/10.1007/BF00377601

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  • DOI: https://doi.org/10.1007/BF00377601

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