一维Cahn-Hilliard方程的几类数值方法比较
发布时间：2018-11-09 17:30
【摘要】：本文针对一维Cahn-Hilliard方程,提出了一种直接间断有限元方法,证明了直接间断有限元格式的保质量守恒性质和保能量衰减性质。对三种有限差分法(Crank-Nicolson Adams-Bashforth方法、基于DVDM的FDM、基于Picard迭代的FDM)和直接间断有限元方法进行了数值比较,我们通过数值算例验证了每种数值格式能够保证质量守恒以及能量衰减,也发现,当时间离散选用向前欧拉时,直接间断有限元方法的时间步长需要取得较小。
[Abstract]:In this paper, a direct discontinuous finite element method is proposed for one dimensional Cahn-Hilliard equation. The conservation of mass and energy conservation of direct discontinuous finite element scheme are proved. Three finite difference methods (Crank-Nicolson Adams-Bashforth method, FDM, based on Picard iteration FDM based on DVDM) and direct discontinuous finite element method (DFEM) are compared numerically. Numerical examples show that each numerical scheme can guarantee the conservation of mass and energy attenuation. It is also found that the time step of direct discontinuous finite element method needs to be smaller when the time discretization is forward Euler.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8
本文编号：2321088
[Abstract]:In this paper, a direct discontinuous finite element method is proposed for one dimensional Cahn-Hilliard equation. The conservation of mass and energy conservation of direct discontinuous finite element scheme are proved. Three finite difference methods (Crank-Nicolson Adams-Bashforth method, FDM, based on Picard iteration FDM based on DVDM) and direct discontinuous finite element method (DFEM) are compared numerically. Numerical examples show that each numerical scheme can guarantee the conservation of mass and energy attenuation. It is also found that the time step of direct discontinuous finite element method needs to be smaller when the time discretization is forward Euler.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8
【参考文献】
相关期刊论文 前2条
1 Ting-chun WANG;Li-mei ZHAO;Bo-ling GUO;;A Class of Stable and Conservative Finite Difference Schemes for the Cahn-Hilliard Equation[J];Acta Mathematicae Applicatae Sinica;2015年04期
2 叶兴德,程晓良;Cahn—Hilliard方程的Legendre谱逼近[J];计算数学;2003年02期
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