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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn-Hilliard Model
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Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn-Hilliard Model

机译：快速，可怕的无条件能量稳定，以及各向异性CAHN-HILLIARD模型的二阶准确算法

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摘要

In this paper, we consider numerical approximations for solving the anisotropic Cahn-Hilliard model. We combine the Scalar Auxiliary Variable (SAV) approach with the stabilization technique to arrive at a novel Stabilized-SAV approach, where three linear stabilization terms, which are shown to be crucial to remove the oscillations caused by the anisotropic coefficient, are added to enhance the stability while keeping the required accuracy. The schemes are very easy-to-implement and fast in the sense that all nonlinear terms are treated in a semi-explicit way, and one only needs to solve three decoupled linear equations with constant coefficients at each time step. We further prove the unconditional energy stabilities rigorously and present numerous 2D and 3D numerical simulations to demonstrate the stability and accuracy. (C) 2019 Published by Elsevier B.V.
机译：在本文中，我们考虑求解各向异性Cahn-Hilliard模型的数值近似。我们将标量辅助变量（SAV）方法与稳定技术相结合，以稳定的稳定保护方法到达，其中三种线性稳定术语被认为是至关重要的，以消除由各向异性系数引起的振荡至关重要，以增强保持所需精度的同时稳定。这些方案非常易于实现，并且在某种意义上快速地以半明确的方式处理所有非线性术语，并且只需要在每个时间步骤求解具有恒定系数的三个去耦线性方程。我们还经过严格证明无条件能量稳定性，并存在许多2D和3D数值模拟，以展示稳定性和准确性。 （c）2019年由elestvier b.v发布。

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