Simulations of dendritic solidification via the diffuse approximate method

Abstract

The current work presents simulations of two-dimensional dendritic solidification via the meshless Diffuse Approximate Method (DAM). The presumed Stefan problem is studied through the phase-field model. Isotropic and anisotropic materials are considered for comparisons with the benchmark tests. Investigations on the change of some constants are carried out to discover their effects on the obtained patterns. The nodal DAM (with the Kronecker delta property of its shape functions) for the spatial discretization and the forward Euler temporal discretization for the coupled phase-field and heat equations provide results that comply with the patterns of previous works. The significant feature of the proposed numerical method manifests through the explicit time marching and the local property of the chosen meshless method that ensues solving small-size linear systems for each subdomain.