A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation

Haiwei Sun; Ning Kang; Jun Zhang; Eric S. Carlson

doi:10.1016/S0378-4754(03)00095-8

A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation

Haiwei Sun, Ning Kang, Jun Zhang, Eric S. Carlson

Computer Science

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

26 Scopus citations

Abstract

We present a fourth-order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two-dimensional convection diffusion equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid method is developed to solve the resulting sparse linear system. Numerical experiments are conducted to verify the fourth-order convergence rate of the derived discretization scheme and to show that the fourth-order compact difference scheme is computationally more efficient than the standard second-order central difference scheme.

Original language	English
Pages (from-to)	651-661
Number of pages	11
Journal	Mathematics and Computers in Simulation
Volume	63
Issue number	6
DOIs	https://doi.org/10.1016/S0378-4754(03)00095-8
State	Published - Nov 24 2003

Bibliographical note

Funding Information:
The research work of the authors was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, ACR-0202934, in part by the US Department of Energy under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology (RIST), and in part by the University of Kentucky Research Committee.

Funding

The research work of the authors was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, ACR-0202934, in part by the US Department of Energy under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology (RIST), and in part by the University of Kentucky Research Committee.

Funders	Funder number
Japanese Research Organization for Information Science & Technology
RIST
US Department of Energy	DE-FG02-02ER45961
US National Science Foundation	CCR-0092532, CCR-9902022, ACR-0202934, CCR-9988165
University of Kentucky Research Committee

Keywords

Convection diffusion equation
Face centered cubic grid
Fourth-order compact scheme
Multigrid method

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Numerical Analysis
Modeling and Simulation
Applied Mathematics

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10.1016/S0378-4754(03)00095-8

Cite this

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title = "A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation",

abstract = "We present a fourth-order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two-dimensional convection diffusion equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid method is developed to solve the resulting sparse linear system. Numerical experiments are conducted to verify the fourth-order convergence rate of the derived discretization scheme and to show that the fourth-order compact difference scheme is computationally more efficient than the standard second-order central difference scheme.",

keywords = "Convection diffusion equation, Face centered cubic grid, Fourth-order compact scheme, Multigrid method",

author = "Haiwei Sun and Ning Kang and Jun Zhang and Carlson, \{Eric S.\}",

note = "Funding Information: The research work of the authors was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, ACR-0202934, in part by the US Department of Energy under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science \& Technology (RIST), and in part by the University of Kentucky Research Committee. ",

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T1 - A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation

AU - Sun, Haiwei

AU - Kang, Ning

AU - Zhang, Jun

AU - Carlson, Eric S.

N1 - Funding Information: The research work of the authors was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, ACR-0202934, in part by the US Department of Energy under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology (RIST), and in part by the University of Kentucky Research Committee.

PY - 2003/11/24

Y1 - 2003/11/24

N2 - We present a fourth-order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two-dimensional convection diffusion equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid method is developed to solve the resulting sparse linear system. Numerical experiments are conducted to verify the fourth-order convergence rate of the derived discretization scheme and to show that the fourth-order compact difference scheme is computationally more efficient than the standard second-order central difference scheme.

AB - We present a fourth-order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two-dimensional convection diffusion equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid method is developed to solve the resulting sparse linear system. Numerical experiments are conducted to verify the fourth-order convergence rate of the derived discretization scheme and to show that the fourth-order compact difference scheme is computationally more efficient than the standard second-order central difference scheme.

KW - Convection diffusion equation

KW - Face centered cubic grid

KW - Fourth-order compact scheme

KW - Multigrid method

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JF - Mathematics and Computers in Simulation

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A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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