Modeling Moving-Boundary Problems of Solidification and Melting Adopting an Arbitrary Lagrangian-Eulerian Approach

Abstract

ABSTRACT We present a new approach for numerically solving three-dimensional moving-boundary problems in solidification and melting adopting a three-dimensional block-structured finite-volume code for collocated grids. An existing moving-grid method for incompressible fluids which satisfies a so-called space conservation law (SCL) was applied in order to account for the fluxes due to the movements of the grids. A consistent formulation of the SCL is presented. The grid mesh was dynamically controlled by a simple parametric sliding-mesh algorithm during the simulations, to avoid highly skewed cells within the domain. This algebraic smoothing algorithm was applied individually within each block of the numerical domain of the block-structured grid. The effectiveness of the method was demonstrated by adopting two different problems of melting/solidification found in the literature. The present interface-tracking algorithm with its adaptive grid technique results in a sharp interface between the melt and the solid phases. Moreover, the computational approach can accommodate large deformations of the solid/melt interface.