Finite difference solutions of solidification phase change problems: Transformed versus fixed grids

In using finite difference techniques for solving diffusion/ convection controlled solidification processes, the numerical discretization is commonly carried out in one of two ways: (1) transformed grid, in which case the physical space is transformed into a solution space that can be discretized with a fixed grid in space; (2) fixed grid, in which case the physical space is discretized with a fixed uniform orthogonal grid and the effects of the phase change are accounted for on the definition of suitable source terms. In this paper, recently proposed transformed- and fixed-grid methods are outlined. The two methods are evaluated based on solving a problem involving the melting of gallium. Comparisons are made between the predictive power of the two methods to resolve the position of the moving phase-change front

[1]  Chie Gau,et al.  Melting and Solidification of a Pure Metal on a Vertical Wall , 1986 .

[2]  Vaughan R Voller,et al.  ENTHALPY-POROSITY TECHNIQUE FOR MODELING CONVECTION-DIFFUSION PHASE CHANGE: APPLICATION TO THE MELTING OF A PURE METAL , 1988 .

[3]  J. Crank.  Free and moving boundary problems , 1984 .

[4]  V. Voller.  FAST IMPLICIT FINITE-DIFFERENCE METHOD FOR THE ANALYSIS OF PHASE CHANGE PROBLEMS , 1990 .

[5]  H. L. Stone.  ITERATIVE SOLUTION OF IMPLICIT APPROXIMATIONS OF MULTIDIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS , 1968 .

[6]  Scott D. Gilmore,et al.  Three-dimensional solidification - A numerical approach , 1988 .

[7]  J. Hsiao,et al.  AN EFFICIENT ALGORITHM FOR FINITE-DIFFERENCE ANALYSES OF HEAT TRANSFER WITH MELTING AND SOLIDIFICATION , 1984 .

[8]  Vaughan R Voller,et al.  Implicit Finite—difference Solutions of the Enthalpy Formulation of Stefan Problems , 1985 .

[9]  E. Sparrow,et al.  Handbook of Numerical Heat Transfer , 1988 .

[10]  Marcel Lacroix,et al.  COMPUTATION OF HEAT TRANSFER DURING MELTING OF A PURE SUBSTANCE FROM AN ISOTHERMAL WALL , 1989 .

[11]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[12]  Christoph Beckermann,et al.  Double-diffusive convection due to melting , 1988 .

[13]  B. W. Webb,et al.  ANALYSIS OF HEAT TRANSFER DURING MELTING OF A PURE METAL FROM AN ISOTHERMAL VERTICAL WALL , 1986 .

[14]  Frank P. Incropera,et al.  A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems. II: Application to solidification in a rectangular cavity , 1987 .

[15]  V. Voller,et al.  A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems , 1987 .

[16]  M. Cross,et al.  An enthalpy method for convection/diffusion phase change , 1987 .

[17]  Ephraim M Sparrow,et al.  Analysis of melting in the presence of natural convection in the melt region , 1977 .

[18]  J. F. Thompson.  Numerical solution of flow problems using body-fitted coordinate systems , 1978 .

[19]  Ashok J. Gadgil,et al.  Analysis of Two-Dimensional Melting in Rectangular Enclosures in Presence of Convection , 1984 .

[20]  F. Incropera,et al.  A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems—I. Model formulation , 1987 .

[21]  V. Voller,et al.  The modelling of heat, mass and solute transport in solidification systems , 1989 .

[22]  H. G. Landau,et al.  Heat conduction in a melting solid , 1950 .

[23]  J. Crank,et al.  TWO METHODS FOR THE NUMERICAL SOLUTION OF MOVING-BOUNDARY PROBLEMS IN DIFFUSION AND HEAT FLOW , 1957 .

[24]  Christoph Beckermann,et al.  Effect of Solid Subcooling on Natural Convection Melting of a Pure Metal , 1989 .