A Positivity-Preserving Finite Volume Scheme for Heat Conduction Equation on Generalized Polyhedral Meshes

doi:10.4208/cicp.OA-2017-0183

	A Positivity-Preserving Finite Volume Scheme for Heat Conduction Equation on Generalized Polyhedral Meshes
	Xie, Hui 1; Xu, Xuejun2,3 ; Zhai, Chuanlei 1; Yong, Heng 1
	2018-11-01
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN	1815-2406
卷号	24 期号:5 页码:1375-1408
摘要	In this paper we present a nonlinear finite volume scheme preserving positivity for heat conduction equations. The scheme uses both cell-centered and cell-vertex unknowns. The cell-vertex unknowns are treated as auxiliary ones and are eliminated by our newly developed second-order explicit interpolation formula on generalized polyhedral meshes. With the help of the additional parameters, it is not necessary to choose the stencil adaptively to obtain the convex decomposition of the co-normal vector and also is not required to replace the interpolation formula with positivity-preserving but usually low-order accurate ones whenever negative interpolated auxiliary unknowns appear. Moreover, the new flux approximation has a fixed stencil. These features make our scheme more efficient compared with other existing methods based on Le Potier's nonlinear two-point approximation, especially in 3D. Numerical experiments show that the scheme maintains the positivity of the continuous solution and has nearly second-order accuracy for the solution on the distorted meshes where the diffusion tensor may be anisotropic and discontinuous.
关键词	Heat conduction anisotropic diffusion tensor distorted mesh positivity-preserving cell-centered scheme vertex elimination
DOI	10.4208/cicp.OA-2017-0183
语种	英语
资助项目	National Natural Science Foundation of China[11371065] ; National Natural Science Foundation of China[11225107] ; Defense Industrial Technology Development Program[B1520132012]
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000455959000005
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32297
专题	计算数学与科学工程计算研究所
通讯作者	Yong, Heng
作者单位	1.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, POB 2719, Beijing 100190, Peoples R China 3.Tongji Univ, Sch Math Sci, Shanghai, Peoples R China
推荐引用方式 GB/T 7714	Xie, Hui,Xu, Xuejun,Zhai, Chuanlei,et al. A Positivity-Preserving Finite Volume Scheme for Heat Conduction Equation on Generalized Polyhedral Meshes[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2018,24(5):1375-1408.
APA	Xie, Hui,Xu, Xuejun,Zhai, Chuanlei,&Yong, Heng.(2018).A Positivity-Preserving Finite Volume Scheme for Heat Conduction Equation on Generalized Polyhedral Meshes.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,24(5),1375-1408.
MLA	Xie, Hui,et al."A Positivity-Preserving Finite Volume Scheme for Heat Conduction Equation on Generalized Polyhedral Meshes".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 24.5(2018):1375-1408.