Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid
- Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, 620000 Ekaterinburg (Russian Federation)
- AO NPO MKM, Ilfata Zakirova st. 24, 426000 Izhevsk (Russian Federation)
We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phase Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.
- OSTI ID:
- 22608265
- Journal Information:
- AIP Conference Proceedings, Vol. 1759, Issue 1; Conference: ICAAM 2016: International conference on analysis and applied mathematics, Almaty (Kazakhstan), 7-10 Sep 2016; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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