A Positivity-Preserving Finite Volume Scheme with Least Square Interpolation for 3D Anisotropic Diffusion Equation

doi:10.1007/s10915-021-01629-2

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	A Positivity-Preserving Finite Volume Scheme with Least Square Interpolation for 3D Anisotropic Diffusion Equation
	Xie, Hui 1; Xu, Xuejun 2,3; Zhai, Chuanlei 1; Yong, Heng 1
	2021-12-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	89 期号:3 页码:25
摘要	In this paper, a new nonlinear finite volume scheme preserving positivity for 3D anisotropic diffusion equation is proposed. A distinct feature of our new scheme is that the auxiliary vertex unknowns appearing in the nonlinear two-point flux approximation are interpolated by the least-square method combined with the so-called correction function. The correction function is local, and only solved when the coefficient discontinuity occurs. Compared with other existing 3D interpolation formulas, our interpolation formula is designed for the general polyhedron mesh and coefficient discontinuity with lower and adaptive computational complexity. The scheme is proven to be positivity-preserving. Numerical examples are presented to demonstrate the second-order accuracy and positivity-preserving property for various anisotropic diffusion problems on the distorted meshes.
关键词	Anisotropic diffusion Positivity Vertex unknowns Least square
DOI	10.1007/s10915-021-01629-2
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11901043,11671048,11671302,11771055]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000707711400001
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59435
专题	中国科学院数学与系统科学研究院
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 with Least Square Interpolation for 3D Anisotropic Diffusion Equation[J]. JOURNAL OF SCIENTIFIC COMPUTING,2021,89(3):25.
APA	Xie, Hui,Xu, Xuejun,Zhai, Chuanlei,&Yong, Heng.(2021).A Positivity-Preserving Finite Volume Scheme with Least Square Interpolation for 3D Anisotropic Diffusion Equation.JOURNAL OF SCIENTIFIC COMPUTING,89(3),25.
MLA	Xie, Hui,et al."A Positivity-Preserving Finite Volume Scheme with Least Square Interpolation for 3D Anisotropic Diffusion Equation".JOURNAL OF SCIENTIFIC COMPUTING 89.3(2021):25.