LONG TIME NUMERICAL SIMULATIONS FOR PHASE-FIELD PROBLEMS USING P-ADAPTIVE SPECTRAL DEFERRED CORRECTION METHODS
LONG TIME NUMERICAL SIMULATIONS FOR PHASE-FIELD PROBLEMS USING P-ADAPTIVE SPECTRAL DEFERRED CORRECTION METHODS
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DOI：
10.1137/130928662
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发表时间：
2015-01-01
影响因子：
3.1
通讯作者：
Yang, Jiang
中科院分区：
文献类型：
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作者：
Feng, Xinlong;Tang, Tao;Yang, Jiang
结合半隐式谱延迟校正（SDC）方法和能量稳定凸分裂技术，提出了一种高阶能量稳定的相场模型模拟方案。本文所采用的凸分裂格式是一种线性无条件稳定方法，但只有一阶精度，因此可以使用SDC方法迭代地提高收敛速度。然而，精度的提高可能会影响相场模型固有的整体能量稳定性。为了降低精度和稳定性，提出了一种局部p自适应策略，通过在可接受的水平上牺牲一些局部能量稳定性来提高精度。所提出的策略是非常有用的产生精确的数值解在小时间（动态）和长时间（稳态）与相当大的时间步长。数值实验证明了所提出的数值策略的有效性。
A high-order and energy stable scheme is developed to simulate phase-field models by combining the semi-implicit spectral deferred correction (SDC) method and the energy stable convex splitting technique. The convex splitting scheme we use here is a linear unconditionally stable method but is only of first-order accuracy, so the SDC method can be used to iteratively improve the rate of convergence. However, it is found that the accuracy improvement may affect the overall energy stability which is intrinsic to the phase-field models. To compromise the accuracy and stability, a local p-adaptive strategy is proposed to enhance the accuracy by sacrificing some local energy stability in an acceptable level. The proposed strategy is found very useful for producing accurate numerical solutions at small time (dynamics) as well as long time (steady state) with reasonably large time stepsizes. Numerical experiments are carried out to demonstrate the high effectiveness of the proposed numerical strategy.