ON THE APPROXIMATION OF THE FOKKER-PLANCK EQUATION OF THE FINITELY EXTENSIBLE NONLINEAR ELASTIC DUMBBELL MODEL I: A NEW WEIGHTED FORMULATION AND AN OPTIMAL SPECTRAL-GALERKIN ALGORITHM IN TWO DIMENSIONS

CORC > 厦门大学 > 数学科学－已发表论文

	ON THE APPROXIMATION OF THE FOKKER-PLANCK EQUATION OF THE FINITELY EXTENSIBLE NONLINEAR ELASTIC DUMBBELL MODEL I: A NEW WEIGHTED FORMULATION AND AN OPTIMAL SPECTRAL-GALERKIN ALGORITHM IN TWO DIMENSIONS
	Shen, Jie ; Yu, Haijun ; Shen J(沈捷)
刊名	http://dx.doi.org/10.1137/100795929
	2012
关键词	DILUTE POLYMER-SOLUTIONS LONG-TIME ASYMPTOTICS GLOBAL WEAK SOLUTIONS DIRECT SOLVERS FENE MODEL FLOWS EXISTENCE POLYNOMIALS SIMULATION 2ND-ORDER
英文摘要	AFOSR [FA9550-08-1-0416]; NFS [DMS-0915066]; National Science Foundation of China [NSFC 11101413]; We propose a new weighted weak formulation for the Fokker-Planck equation of the finitely extensible nonlinear elastic dumbbell model and prove its well-posedness in weighted Sobolev spaces. We also propose simple and efficient semi-implicit time-discretization schemes which are unconditionally stable, i.e., the step size of time marching does not depend on the number of the bases used in configurational space. We then restrict ourselves to the two-dimensional case and construct two Fourier-Jacobi spectral-Galerkin algorithms which enjoy the following properties: (i) they are unconditionally stable, spectrally accurate, and of optimal computational complexity; (ii) they conserve the volume and provide accurate approximation to higher-order moments of the distribution function; and (iii) they can be easily extended to coupled nonhomogeneous systems. Numerical results are presented to show how to choose a proper weight to get the best numerical results of the distribution function and the polymer stress.
语种	英语
出版者	SIAM J NUMER ANAL
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/90962]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Shen, Jie,Yu, Haijun,Shen J. ON THE APPROXIMATION OF THE FOKKER-PLANCK EQUATION OF THE FINITELY EXTENSIBLE NONLINEAR ELASTIC DUMBBELL MODEL I: A NEW WEIGHTED FORMULATION AND AN OPTIMAL SPECTRAL-GALERKIN ALGORITHM IN TWO DIMENSIONS[J]. http://dx.doi.org/10.1137/100795929,2012.
APA	Shen, Jie,Yu, Haijun,&沈捷.(2012).ON THE APPROXIMATION OF THE FOKKER-PLANCK EQUATION OF THE FINITELY EXTENSIBLE NONLINEAR ELASTIC DUMBBELL MODEL I: A NEW WEIGHTED FORMULATION AND AN OPTIMAL SPECTRAL-GALERKIN ALGORITHM IN TWO DIMENSIONS.http://dx.doi.org/10.1137/100795929.
MLA	Shen, Jie,et al."ON THE APPROXIMATION OF THE FOKKER-PLANCK EQUATION OF THE FINITELY EXTENSIBLE NONLINEAR ELASTIC DUMBBELL MODEL I: A NEW WEIGHTED FORMULATION AND AN OPTIMAL SPECTRAL-GALERKIN ALGORITHM IN TWO DIMENSIONS".http://dx.doi.org/10.1137/100795929 (2012).