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首页> 外文期刊>International Journal of Heat and Mass Transfer >Fully-discrete spectral-Galerkin scheme with decoupled structure and second-order time accuracy for the anisotropic phase-field dendritic crystal growth model
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Fully-discrete spectral-Galerkin scheme with decoupled structure and second-order time accuracy for the anisotropic phase-field dendritic crystal growth model

机译：具有去耦结构的完全离散的光谱 - Galerkin方案和各向异性相位导晶晶体生长模型的二阶时间精度

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In this work, we consider numerical approximations of the anisotropic phase-field dendritic crystal growth model, which is a highly complex coupled nonlinear system consisting of the anisotropic Allen-Cahn equation and the heat equation. Through the combination of a novel explicit auxiliary variable IEQ approach for temporal discretization and the spectral-Galerkin approach for spatial discretization, we develop the first fully-discrete numerical scheme with linearity, decoupled structure, unconditional energy stability, and second-order time accuracy for the particular phase-field dendritic model. In the process of obtaining a full decoupling structure and maintaining energy stability, the introduction of two auxiliary variables and the design of two auxiliary ODEs play a vital role. The designed scheme is highly efficient because only a few elliptic equations with constant coefficients are needed to be solved at each time step. The unconditional energy stability of the scheme has been strictly proved, and the detailed implementation process is given. Through several numerical simulations of 2D and 3D dendritic crystal growth examples, we further verify the convergence rate, energy stability, and effectiveness of the developed algorithm.
机译：在这项工作中，我们考虑各向异性相位树枝状晶体生长模型的数值近似，其是由各向异性艾伦-CAHN方程和热方程组成的高度复杂的耦合非线性系统。通过新颖的明确辅助变量IEQ方法进行时间离散化和用于空间离散化的光谱 - Galerkin方法，我们开发了具有线性，分离结构，无条件能量稳定性和二阶时间精度的第一全离散数值方案特定的阶段场树枝状模型。在获得完全去耦结构和保持能量稳定性的过程中，引入两个辅助变量和两个辅助杂散的设计起到了重要作用。设计方案高效，因为在每次步骤中仅需要省略几个具有恒定系数的椭圆方程。严格证明了该计划的无条件能量稳定性，并提供了详细的实施过程。通过若干数值模拟的2D和3D树突晶体生长实施例，我们进一步验证了发达算法的收敛速率，能量稳定性和有效性。

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