A high-order modified finite-volume method on Cartesian grids for nonlinear convection-diffusion problems

doi:10.1007/s40314-020-01253-0

CSpace

	A high-order modified finite-volume method on Cartesian grids for nonlinear convection-diffusion problems
	Du, Yulong 1; Wang, Yahui 2,3,4; Yuan, Li 2,3,4
	2020-07-14
发表期刊	COMPUTATIONAL & APPLIED MATHEMATICS
ISSN	2238-3603
卷号	39 期号:3 页码:20
摘要	Recently, Buchmuller and Helzel proposed a modified dimension-by-dimension finite-volume (FV) WENO method on Cartesian grids for multidimensional nonlinear conservation laws which can retain the full order of accuracy of the underlying one-dimensional (1D) reconstruction. In this work, we extend this method to multidimensional convection-diffusion equations. The 1D sixth-order central reconstruction of the conserved quantity is utilized for discretizing the diffusion terms in which the diffusion coefficients may be nonlinear functions of the conserved quantity. Using high-order accurate conversions between edge-averaged values and edge center values of any sufficiently smooth quantity, high-order accurate convective and viscous numerical fluxes at cell interfaces are computed. The present modified FV method uses fourth-order accurate conversions for the diffusive fluxes. Numerical examples show that the present method achieves fourth-order accuracy for multidimensional smooth problems, and is suitable for the numerical simulation of viscous shocked flows.
关键词	Finite-volume method High-order accuracy Dimension-by-dimension reconstruction Cartesian grid Nonlinear convection-diffusion equation 65M08 65M12 65M20
DOI	10.1007/s40314-020-01253-0
收录类别	SCI
语种	英语
资助项目	Natural Science Foundation of China[91641107] ; Natural Science Foundation of China[91852116] ; Fundamental Research of Civil Aircraft[MJ-F-2012-04]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000553137100005
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51871
专题	中国科学院数学与系统科学研究院
通讯作者	Yuan, Li
作者单位	1.Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Du, Yulong,Wang, Yahui,Yuan, Li. A high-order modified finite-volume method on Cartesian grids for nonlinear convection-diffusion problems[J]. COMPUTATIONAL & APPLIED MATHEMATICS,2020,39(3):20.
APA	Du, Yulong,Wang, Yahui,&Yuan, Li.(2020).A high-order modified finite-volume method on Cartesian grids for nonlinear convection-diffusion problems.COMPUTATIONAL & APPLIED MATHEMATICS,39(3),20.
MLA	Du, Yulong,et al."A high-order modified finite-volume method on Cartesian grids for nonlinear convection-diffusion problems".COMPUTATIONAL & APPLIED MATHEMATICS 39.3(2020):20.