A comparison of methods for the calculation of interface curvature in two-dimensional cellular automata solidification models

Abstract

Four methods for the calculation of interface curvature in cellular automata models for solidification are evaluated. Three of the methods are based on the level-set interpretation of the solid fraction field and calculate the required spatial derivatives by finite differences or by a Taylor approximation in different neighborhoods. The fourth method is the height function method, an interface reconstruction method based on the row- or columnwise summation of solid fractions.Two benchmark problems are investigated, representative for two types of cellular automata models for solidification where interface cells exist in either Moore or von Neumann neighborhoods of solid cells. For the case of interface cells in the Moore neighborhood of solid cells, the height function method yields the most accurate results, while all level-set based methods exhibit significant numerical scatter. For the case of interface cells existing in the von Neumann neighborhood of solid cells, all methods yield a higher level of numerical scatter. The best curvature calculations for this case are achieved by the height function method and by the level set method with a Taylor approximation in an extended neighborhood.