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	对两类带有非局部项的水波模型的半隐式谱缺陷校正法及其衰减性质的数值研究; A semi-implicit spectral deferred correction method for two water wave models with nonlocal viscous term and numerical study of their decay rates
	毛志平 ; 沈捷
	2015-08-20
关键词	水波 衰减率 半隐式 谱缺陷校正 water wave nonlocal decay rate semi-implicit spectral deferred correction
英文摘要	本文主要对两类带非局部项水波模型的衰减性质进行数值研究,第一类模型是具有时间非局部黏性项的kdV型方程:u_T+u_X+βu_(XXX)+V~(1/2)/π~(1/2)∫TOu_T(S)/T-X~(1/2)+uu_X=Vu_(XX),另一类为空间非局部黏性扩散-色散的kAkuTAnI-MATSuuCHI模型:u_T+βu_(TXX)V(d~(1/2)+f~(-1))(I|ζ|~(1/2)SIgn(ζ)u(ζ)))+γuu_X=0.对这两类水波模型的离散,在空间上,本文采用fOurIEr变换;在时间上,则结合半隐式格式的计算方便性和谱缺陷校正法的高阶性质,采用半隐式谱缺陷校正法(SISdC).通过一系列的数值试验,本文研究模型中黏性项、几何色散项、非线性项和计算区域大小等对水波衰减性质的影响.; In this paper,we numerically investigate the decay rates of two nonlocal water wave models.One is in the KdV form with a time nonlocal viscous dispersive term u_t+u_x+ βu_(xxx)+v~(1/2)/π~(1/2)∫to u_t(s)/(t-s)~(1/2)ds+uu_x=vu_(xx)Another is the spatial nonlocal viscous diffusion-dispersive Kakutani-Matsuuchi model u_t- βu_(txx) + v(D~1/2 +F~(1/2)(i|ζ|~(1/2)sign(ζ)u(ζ)))+γuu_x = 0.For the discretization of these two models,we use Fourier method in spatial,while in temporal,with the help of computational conveniences of semi-implicit and high order property of spectral defect correction,we a semiimplicit spectral defect correction(SISDC) method.Then we study the influences of viscous,geometric dispersion,nonlinearity and computational domain size by plenty of numerical experiment.; 国家自然科学基金(批准号:91130002和11371298)资助项目
语种	zh_CN
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/119917]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	毛志平,沈捷. 对两类带有非局部项的水波模型的半隐式谱缺陷校正法及其衰减性质的数值研究, A semi-implicit spectral deferred correction method for two water wave models with nonlocal viscous term and numerical study of their decay rates[J],2015.
APA	毛志平,&沈捷.(2015).对两类带有非局部项的水波模型的半隐式谱缺陷校正法及其衰减性质的数值研究..
MLA	毛志平,et al."对两类带有非局部项的水波模型的半隐式谱缺陷校正法及其衰减性质的数值研究".(2015).

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