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PHYSICAL REVIEW E, VOLUME 64, 041602
Phase field model for three-dimensional dendritic growth with fluid flow
Jun-Ho Jeong,1 Nigel Goldenfeld,2 and Jonathan A. Dantzig1
1
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
2Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Received 3 May 2001; published 20 September 2001
We study the effect of fluid flow on three-dimensional 3D dendrite growth using a phase-field model on an
adaptive finite-element grid. In order to simulate 3D fluid flow, we use an averaging method for the flow
problem coupled to the phase-field method and the semi-implicit approximated projection method SIAPM. We
describe a parallel implementation for the algorithm, using the CHARM FEM framework, and demonstrate its
efficiency. We introduce an improved method for extracting dendrite tip position and tip radius, facilitating
accurate comparison to theory. We benchmark our results for 2D dendrite growth with solvability theory and
previous results, finding them to be in good agreement. The physics of dendritic growth with fluid flow in three
dimensions is very different from that in two dimensions, and we discuss the origin of this behavior.
DOI: 10.1103/PhysRevE.64.041602 PACS numbers: 81.10.Aj, 05.70.Ln, 81.30.Fb, 64.70.Dv
I. INTRODUCTION nominally perpendicular to their primary growth direction.
The m
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