High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates

Jan Nordström; Mark H. Carpenter

doi:10.1006/jcph.2001.6864

High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates

Jan Nordström, Mark H. Carpenter

Research output: Contribution to journal › Article › peer-review

134 Citations (Scopus)

Abstract

Boundary and interface conditions are derived for high-order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. Difficulties presented by the combination of multiple dimensions and varying coefficients are analyzed. In particular, problems related to nondiagonal norms, a varying Jacobian, and varying and vanishing wave speeds are considered. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

Original language	English
Pages (from-to)	149-174
Number of pages	26
Journal	Journal of Computational Physics
Volume	173
Issue number	1
DOIs	https://doi.org/10.1006/jcph.2001.6864
Publication status	Published - 10 Oct 2001
Externally published	Yes

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

Access to Document

10.1006/jcph.2001.6864

Cite this

@article{f38474b0bc2241deb642e078a0aed69e,

title = "High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates",

abstract = "Boundary and interface conditions are derived for high-order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. Difficulties presented by the combination of multiple dimensions and varying coefficients are analyzed. In particular, problems related to nondiagonal norms, a varying Jacobian, and varying and vanishing wave speeds are considered. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.",

author = "Jan Nordstr{\"o}m and Carpenter, {Mark H.}",

year = "2001",

month = oct,

day = "10",

doi = "10.1006/jcph.2001.6864",

language = "English",

volume = "173",

pages = "149--174",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates

AU - Nordström, Jan

AU - Carpenter, Mark H.

PY - 2001/10/10

Y1 - 2001/10/10

N2 - Boundary and interface conditions are derived for high-order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. Difficulties presented by the combination of multiple dimensions and varying coefficients are analyzed. In particular, problems related to nondiagonal norms, a varying Jacobian, and varying and vanishing wave speeds are considered. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

AB - Boundary and interface conditions are derived for high-order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. Difficulties presented by the combination of multiple dimensions and varying coefficients are analyzed. In particular, problems related to nondiagonal norms, a varying Jacobian, and varying and vanishing wave speeds are considered. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

UR - http://www.scopus.com/inward/record.url?scp=0035841069&partnerID=8YFLogxK

U2 - 10.1006/jcph.2001.6864

DO - 10.1006/jcph.2001.6864

M3 - Article

AN - SCOPUS:0035841069

SN - 0021-9991

VL - 173

SP - 149

EP - 174

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this