Abstract
In this paper, we present several numerical simulation results of dendritic pattern formation using an isotropic crystal growth model, which is based on phase-field modeling, on curved surfaces. An explicit time-stepping method is used and the direct computing method to the Laplace–Beltrami operator, which employs the point centered triangulation approximating Laplacian over the discretized surface with a triangular mesh, is adopted. Numerical simulations are performed not only on simple but also on complex surfaces with various curvatures, and the proposed method can simulate dendritic growth on complex surfaces. In particular, ice crystal growth simulation results on aircraft fuselage or metal bell-shaped curved surfaces are provided in order to demonstrate the practical relevance to our dendrite growth model. Furthermore, we perform several numerical parameter tests to obtain a best fitted set of parameters on simple surfaces. Finally, we apply this set of parameters to numerical simulation on complex surfaces.
Highlights
The beauty of nature’s crystals has led many researchers to investigate them over the past decades
The phase-field method has been widely applied in numerical simulation of dendritic crystal growth model [7,8,9,10,11], most literatures only consider the solidification of pure substances in undercooled melts in two- and three-dimensional spaces; not on curved surfaces
We present several numerical simulation results of an isotropic crystal growth model, which is based on phase-field approach, on curved surfaces with triangular discretizations
Summary
The beauty of nature’s crystals has led many researchers to investigate them over the past decades. The phase-field method has been widely applied in numerical simulation of dendritic crystal growth model [7,8,9,10,11], most literatures only consider the solidification of pure substances in undercooled melts in two- and three-dimensional spaces; not on curved surfaces. Using the phase-field method, for instance, the authors in [12] successfully simulate the crystal growth with an anisotropic diffusion scheme in two dimensional space. In the study of [17], robust and fast phase-field simulations of dendritic crystal growth are performed in both two- and three-dimensional spaces, their computational results are consistent with the numerical experiments. We present several numerical simulation results of an isotropic crystal growth model, which is based on phase-field approach, on curved surfaces with triangular discretizations.
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