References
- J. Crank , Free and Moving Boundary Problems , Clarendon Press , Oxford , chaps. 3 and 6 , 1984 .
- N. Shamsundar , Comparison of Numerical Methods for Diffusion Problems with Moving Boundaries , in D. G. Wilson and P. T. Boggs (eds.) , Moving Boundary Problems , Academic Press , New York , pp. 165 – 185 , 1978 .
- R. M. Furzeland , A Comparative Study of-Numerical Methods for Moving Boundary Problems , J. Inst. Math. Appl. vol. 26 , pp. 411 – 429 , 1980 .
- D. Poirier , M. Salcudean , On Numerical Methods Used in Mathematical Modeling of Phase Change in Liquid Metals , J. Heat Transfer Trans. ASME. vol. 110 , pp. 562 – 570 , 1980 .
- R. W. Lewis and P. M. Roberts , Finite Element Simulation of Solidification Problems , Appl Sci. Res. , vol. 44 , pp. 61 – 92 , 1987 .
- J. A. Dantzig , Modeling Liquid-Solid Phase Changes with Melt Convection , Int. J. Numer. Meth. Eng. , vol. 28 , pp. 1769 – 1785 , 1989 .
- V. R. Voller and C. R. Swaminathan , Fixed Grid Techniques for Phase Change Problems A Review , Int. J. Numer. Meth. Eng. , vol. 30 , pp. 875 – 898 , 1990 .
- V. R. Voller , Finite Difference Solutions of Solidification Phase Change Problems Transformed Versus Fixed Grid , Numer. Heat Transf., Part B , vol. 17 , pp. 25 – 41 , 1990 .
- K. K. Tamma and R. R. Namburu , Recent Advances, Trends and New Perspectives via Enthalpy-Based Finite Element Formulations for Applications to Solidification Problems , Int. J. Numer. Meth. Eng. , vol. 30 , pp. 803 – 820 , 1990 .
- V. R. Voller and C. R. Swaminathan , General Source-Based Method for Solidification Phase Change , Numer. Heat Transfer, Part B , vol. 19 , pp. 175 – 189 , 1991 .
- C. Bonacina , G. Comini , A. Fasano ,M, Primicerio, Numerical Solution of Phase-Change Problems , Int. J. Heat Mass Transfer , vol. 16 , pp. 1825 – 1832 , 1973 .
- Q. T. Priam , The Use of Lumped Capacitance in the Finite-Element Solution of Heat Conduction Problems with Phase Change , Int. J. Heat Mass Transfer , vol. 29 , pp. 285 – 291 , 1986 .
- G. Comini , S. Del Giudice , and O. Saro , A Conservative Algorithm for Multidimensional Conduction Phase Change , Int. J. Numer. Meth. Eng. , vol. 30 , pp. 697 – 709 , 1990 .
- E. C. Lemmon , Phase Change Techniques for Finite Element Conduction Codes , in Numerical Methods in Thermal Problems ( Proc. Conf. ), July 1979 , Swansea , Pineridge Press , Swansea , pp. 149 – 158 , 1979 .
- K. Mogan , R. W. Lewis , and O. C. Zienkiewicz , An Improved Algorithm for Heat Conduction Problem with Phase Change , Int. J. Numer. Meth. Eng. , vol. 12 , pp. 1191 – 1195 , 1978 .
- O. C. Zienkiewicz and K. Morgan , Finite Element and Approximation , John Wiley , New York , chap. 7 , 1983 .
- D. J. R. Owen and F. Damjanic , Reduced Numerical Integration in Thermal Transient Finite Element Analysis , Comp. & Struct. , vol. 17 , pp. 261 – 276 , 1983 .
- A. J. Dalhuijsen and A. Segal , Comparison of Finite Element Techniques for Solidification Problems , Int. J. Numer. Meth. Eng. , vol. 23 , pp. 1807 – 1829 , 1986 .
- M. S. Engelman , FIDAP Theoretical Manual , Fluid Dynamics International , Evanston , Ill. , 1991 .
- V. R. Voller , Fast Implicit Finite-Difference Methods for the Analysis of Phase Change Problems , Numer. Heat Transfer, Part B , vol. 17 , pp. 155 – 169 , 1990 .
- C. M. Brauner , M. Fremond and B. Nicoiaenko , A New Homographic Approximation to Multiphase Stefan Problems , in A. Fasano and M. Primicerio (eds.) , Free Boundary Problems Theory and Applications , Elsevier , Amsterdam , pp. 365 – 379 , 1982 ,
- D. Blanchard and M. Fremond , The Stefan Problem Computing Without the Free Boundary , Int. J. Numer. Meth. Eng. , vol. 20 , pp. 757 – 771 , 1984 .
- M. Yao and A. Chait , Application of the Homographic Approximation in the Enthalpy Method for Phase Change Problems , Int. J. Numer. Meth. Heat & Fluid Flow. vol. 3 , pp. 157 – 172 , 1993 .
- R. D. Cook , D. S. Malkus , and M. E. Plesha , Concepts and Applications of Finite Element Analysis , 3rd ed. , John Wiley , New York , 1989 .
- A. V. Luikov , Analytical Heat Diffusion Theory , Academic Press , New York , 1968 .
- C. Elliott , Eddy Structure in Turbulent Flow , D. Phil, thesis , Oxford University , 1976 .
- R. M. Furzeland , The Numerical Solution of Two-Dimensional Moving Boundary Problems Using Curvilinear Coordinate Transformation , Ph.D. thesis , Brunei University ; also Brunei University Math. Rep. TR/77 , 1977 .
- M. Yao and A. Chait , A Numerical Study of the Enthalpy Method , in preparation , 1993 .