High order compact scheme with multigrid local mesh refinement procedure for convection diffusion problems

Jun Zhang; Haiwei Sun; Jennifer J. Zhao

doi:10.1016/S0045-7825(02)00398-5

High order compact scheme with multigrid local mesh refinement procedure for convection diffusion problems

Jun Zhang
, Haiwei Sun
, Jennifer J. Zhao

Computer Science

Producción científica: Article › revisión exhaustiva

54 Citas (Scopus)

Resumen

We derive a new fourth order compact finite difference scheme which allows different meshsize in different coordinate directions for the two-dimensional convection diffusion equation. A multilevel local mesh refinement strategy is used to deal with the local singularity problem. A corresponding multilevel multigrid method is designed to solve the resulting sparse linear system. Numerical experiments are conducted to show that the local mesh refinement strategy works well with the high order compact discretization scheme to recover high order accuracy for the computed solution. Our solution method is also shown to be effective and robust with respect to the level of mesh refinement and the anisotropy of the problems.

Idioma original	English
Páginas (desde-hasta)	4661-4674
Número de páginas	14
Publicación	Computer Methods in Applied Mechanics and Engineering
Volumen	191
N.º	41-42
DOI	https://doi.org/10.1016/S0045-7825(02)00398-5
Estado	Published - sept 13 2002

Nota bibliográfica

Funding Information:
Jun Zhang’s research work was supported in part by the U.S. National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, CCR-0117602, in part by the Japan Research Organization for Information Science & Technology, and in part by the University of Kentucky Center for Computational Sciences. Haiwei Sun’s research work was supported by U.S. National Science Foundation under grant CCR-9988165. Jennifer J. Zhao’s research work was supported by the U.S. National Science Foundation under grant CCR-0117602.

Financiación

Jun Zhang’s research work was supported in part by the U.S. National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, CCR-0117602, in part by the Japan Research Organization for Information Science & Technology, and in part by the University of Kentucky Center for Computational Sciences. Haiwei Sun’s research work was supported by U.S. National Science Foundation under grant CCR-9988165. Jennifer J. Zhao’s research work was supported by the U.S. National Science Foundation under grant CCR-0117602.

Financiadores	Número del financiador
Japan Research Organization for Information Science and Technology
National Science Foundation (NSF)	CCR-0092532, CCR-9902022, CCR-0117602, CCR-9988165
University of Kentucky Information Technology Department and Center for Computational Sciences

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/S0045-7825(02)00398-5

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@article{bc341da7c075409dac70522ac4765677,

title = "High order compact scheme with multigrid local mesh refinement procedure for convection diffusion problems",

abstract = "We derive a new fourth order compact finite difference scheme which allows different meshsize in different coordinate directions for the two-dimensional convection diffusion equation. A multilevel local mesh refinement strategy is used to deal with the local singularity problem. A corresponding multilevel multigrid method is designed to solve the resulting sparse linear system. Numerical experiments are conducted to show that the local mesh refinement strategy works well with the high order compact discretization scheme to recover high order accuracy for the computed solution. Our solution method is also shown to be effective and robust with respect to the level of mesh refinement and the anisotropy of the problems.",

keywords = "Convection diffusion equation, Local mesh refinement, Multigrid method, Singularity and boundary layer",

author = "Jun Zhang and Haiwei Sun and Zhao, \{Jennifer J.\}",

note = "Funding Information: Jun Zhang{\textquoteright}s research work was supported in part by the U.S. National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, CCR-0117602, in part by the Japan Research Organization for Information Science \& Technology, and in part by the University of Kentucky Center for Computational Sciences. Haiwei Sun{\textquoteright}s research work was supported by U.S. National Science Foundation under grant CCR-9988165. Jennifer J. Zhao{\textquoteright}s research work was supported by the U.S. National Science Foundation under grant CCR-0117602.",

year = "2002",

month = sep,

day = "13",

doi = "10.1016/S0045-7825(02)00398-5",

language = "English",

volume = "191",

pages = "4661--4674",

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TY - JOUR

T1 - High order compact scheme with multigrid local mesh refinement procedure for convection diffusion problems

AU - Zhang, Jun

AU - Sun, Haiwei

AU - Zhao, Jennifer J.

N1 - Funding Information: Jun Zhang’s research work was supported in part by the U.S. National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, CCR-0117602, in part by the Japan Research Organization for Information Science & Technology, and in part by the University of Kentucky Center for Computational Sciences. Haiwei Sun’s research work was supported by U.S. National Science Foundation under grant CCR-9988165. Jennifer J. Zhao’s research work was supported by the U.S. National Science Foundation under grant CCR-0117602.

PY - 2002/9/13

Y1 - 2002/9/13

N2 - We derive a new fourth order compact finite difference scheme which allows different meshsize in different coordinate directions for the two-dimensional convection diffusion equation. A multilevel local mesh refinement strategy is used to deal with the local singularity problem. A corresponding multilevel multigrid method is designed to solve the resulting sparse linear system. Numerical experiments are conducted to show that the local mesh refinement strategy works well with the high order compact discretization scheme to recover high order accuracy for the computed solution. Our solution method is also shown to be effective and robust with respect to the level of mesh refinement and the anisotropy of the problems.

AB - We derive a new fourth order compact finite difference scheme which allows different meshsize in different coordinate directions for the two-dimensional convection diffusion equation. A multilevel local mesh refinement strategy is used to deal with the local singularity problem. A corresponding multilevel multigrid method is designed to solve the resulting sparse linear system. Numerical experiments are conducted to show that the local mesh refinement strategy works well with the high order compact discretization scheme to recover high order accuracy for the computed solution. Our solution method is also shown to be effective and robust with respect to the level of mesh refinement and the anisotropy of the problems.

KW - Convection diffusion equation

KW - Local mesh refinement

KW - Multigrid method

KW - Singularity and boundary layer

UR - https://www.scopus.com/pages/publications/0037073035

UR - https://www.scopus.com/pages/publications/0037073035#tab=citedBy

U2 - 10.1016/S0045-7825(02)00398-5

DO - 10.1016/S0045-7825(02)00398-5

M3 - Article

AN - SCOPUS:0037073035

SN - 0045-7825

VL - 191

SP - 4661

EP - 4674

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 41-42

ER -

High order compact scheme with multigrid local mesh refinement procedure for convection diffusion problems

Resumen

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Financiación

ASJC Scopus subject areas

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