Simulation of ice formation by the finite volume method

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.

Keywords

• phase change
• fixed grid
• latent heat
• finite volume method