广义分数阶Allen-Cahn相场方程的数值模拟研究

来源 :数学理论与应用 | 被引量 : 0次 | 上传用户：wuhanchi

【摘要】

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相场既是一种应用模型也是一种研究方法,在材料微结构演化等实际问题中有广泛应用.本文首先建立广义分数阶Allen-Cahn相场方程模型,并采用有限差分方法在时间和空间上对模型进行离散,得到相应的离散格式;其次分别对整数阶、分数阶和广义分数阶的Allen-Cahn方程进行数值模拟,通过数值结果验证本文所建立的广义分数阶模型的有效性;最后探讨界面宽度对Allen-Cahn相场方程的数值解的影响.本文从广义分数阶基本原理出发,拓宽了相场方程的研究范围,对材料微结构演化研究有重要意义.

【作者】

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吴函宇都昌发刘雨婷郑洲顺

【机构】

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中南大学数学与统计学院,长沙,410083

【出处】

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数学理论与应用

【发表日期】

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2020年2期

【关键词】

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广义分数阶相场方法有限差分法材料微结构演化

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广义分数阶Allen-Cahn相场方程的数值模拟研究

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