Rotchana Prapainop and Kuntinee Maneeratana

pp. 55 - 70

Abstract

This paper investigates the simulation of ice formation in one and two dimensions by the cell-centred
finite volume method. The model is based on the heat conduction equation with the fixed grid, latent heat
source approach. The piecewise-linear profile of variables in space is employed. For the temporal discretisation, three time-stepping schemes are compared: the explicit, Crank-Nicolson, and the fully implicit schemes.
Also examined are different approximations of conductivity at interfaces between adjacent ice and water
control volumes, i.e. the 2 well established arithmetic and harmonic means of ice and water conductivities;
while the use of ice conductivity is introduced. It is found that numerical results of all temporal schemes show
excellent agreements with analytical solutions and exhibit similar accuracies once grid and time interval
independencies are achieved. The explicit scheme, however, has superior CPU-time efficiency. For the investigation on the interface conductivity, the conductivity approximation as that of ice yields the most accurate
computed temperature field.