A 15-point high-order compact scheme with multigrid computation for solving 3D convection diffusion equations

Yin Wang; Su Yu; Ruxin Dai; Jun Zhang

doi:10.1080/00207160.2014.893296

A 15-point high-order compact scheme with multigrid computation for solving 3D convection diffusion equations

Yin Wang, Su Yu, Ruxin Dai, Jun Zhang

Computer Science

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

3 Scopus citations

Abstract

We propose a method with sixth-order accuracy to solve the three-dimensional (3D) convection diffusion equation. We first use a 15-point fourth-order compact discretization scheme to obtain fourth-order solutions on both fine and coarse grids using the multigrid method. Then an iterative mesh refinement technique combined with Richardson extrapolation is used to approximate the sixth-order accurate solution on the fine grid. Numerical results are presented for a variety of test cases to demonstrate the efficiency and accuracy of the proposed method, compared with the standard fourth-order compact scheme.

Original language	English
Pages (from-to)	411-423
Number of pages	13
Journal	International Journal of Computer Mathematics
Volume	92
Issue number	2
DOIs	https://doi.org/10.1080/00207160.2014.893296
State	Published - Feb 1 2015

Bibliographical note

Publisher Copyright:
© 2014, © 2014 Taylor & Francis.

Keywords

15-point stencil
Reynolds number
convection diffusion equation
multigrid method
sixth-order compact scheme

ASJC Scopus subject areas

Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.1080/00207160.2014.893296

Cite this

@article{1b234a508150426d8a0c03049701f130,

title = "A 15-point high-order compact scheme with multigrid computation for solving 3D convection diffusion equations",

abstract = "We propose a method with sixth-order accuracy to solve the three-dimensional (3D) convection diffusion equation. We first use a 15-point fourth-order compact discretization scheme to obtain fourth-order solutions on both fine and coarse grids using the multigrid method. Then an iterative mesh refinement technique combined with Richardson extrapolation is used to approximate the sixth-order accurate solution on the fine grid. Numerical results are presented for a variety of test cases to demonstrate the efficiency and accuracy of the proposed method, compared with the standard fourth-order compact scheme.",

keywords = "15-point stencil, Reynolds number, convection diffusion equation, multigrid method, sixth-order compact scheme",

author = "Yin Wang and Su Yu and Ruxin Dai and Jun Zhang",

note = "Publisher Copyright: {\textcopyright} 2014, {\textcopyright} 2014 Taylor & Francis.",

year = "2015",

month = feb,

day = "1",

doi = "10.1080/00207160.2014.893296",

language = "English",

volume = "92",

pages = "411--423",

number = "2",

}

TY - JOUR

T1 - A 15-point high-order compact scheme with multigrid computation for solving 3D convection diffusion equations

AU - Wang, Yin

AU - Yu, Su

AU - Dai, Ruxin

AU - Zhang, Jun

PY - 2015/2/1

Y1 - 2015/2/1

N2 - We propose a method with sixth-order accuracy to solve the three-dimensional (3D) convection diffusion equation. We first use a 15-point fourth-order compact discretization scheme to obtain fourth-order solutions on both fine and coarse grids using the multigrid method. Then an iterative mesh refinement technique combined with Richardson extrapolation is used to approximate the sixth-order accurate solution on the fine grid. Numerical results are presented for a variety of test cases to demonstrate the efficiency and accuracy of the proposed method, compared with the standard fourth-order compact scheme.

AB - We propose a method with sixth-order accuracy to solve the three-dimensional (3D) convection diffusion equation. We first use a 15-point fourth-order compact discretization scheme to obtain fourth-order solutions on both fine and coarse grids using the multigrid method. Then an iterative mesh refinement technique combined with Richardson extrapolation is used to approximate the sixth-order accurate solution on the fine grid. Numerical results are presented for a variety of test cases to demonstrate the efficiency and accuracy of the proposed method, compared with the standard fourth-order compact scheme.

KW - 15-point stencil

KW - Reynolds number

KW - convection diffusion equation

KW - multigrid method

KW - sixth-order compact scheme

UR - http://www.scopus.com/inward/record.url?scp=84920507895&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920507895&partnerID=8YFLogxK

U2 - 10.1080/00207160.2014.893296

DO - 10.1080/00207160.2014.893296

M3 - Article

AN - SCOPUS:84920507895

SN - 0020-7160

VL - 92

SP - 411

EP - 423

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 2

ER -

A 15-point high-order compact scheme with multigrid computation for solving 3D convection diffusion equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this