A parallel finite volume procedure for phase-field simulation of solidification

Abstract

We describe an implementation detail of a parallel finite volume solver PPFF2 (2-dimensional parallel phase-field finite volume method solver) for the simulation of solidification in two dimensions using the phase-field model. The governing equations for phase-field and temperature field are discretized with cell-centered finite volume method in a fully implicit way. In each time step, a parallel version strongly implicit procedure is used to solve the discretized equations. The problem of the growth of a solid seed into an undercooled melt is first solved to validate the numerical algorithm. The effects of the dimensionless width $ϵ$ (0.0025, 0.0020, 0.0015) and mesh spacing $\Delta x$ ($2ϵ,1.5ϵ,1.0ϵ$) on the structures of dendrites and interface growth rate are investigated. At last, the competitive growth of the second and ternary arms with different noise term are simulated with the parallel finite volume code developed in this work. In terms of the parallel performance, the maximum speed-up for $2000\times 2000,$ 3$000\times 3000$ grid systems are 6.98 and 8.77, its corresponding efficiency 43.6% and 54.8%.