An Efficient Parallel Algorithm with Application to Computational Fluid Dynamics

W. Rivera; Jianping Zhu; D. Huddleston

doi:10.1016/S0898-1221(03)80013-5

An Efficient Parallel Algorithm with Application to Computational Fluid Dynamics

W. Rivera
, Jianping Zhu
, D. Huddleston

University of Puerto Rico - Mayaguez
Mississippi State University

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

Abstract

When solving time-dependent partial differential equations on parallel computers using the nonoverlapping domain decomposition method, one often needs numerical boundary conditions on the boundaries between subdomains. These numerical boundary conditions can significantly affect the stability and accuracy of the final algorithm. In this paper, a stability and accuracy analysis of the existing methods for generating numerical boundary conditions will be presented, and a new approach based on explicit predictors and implicit correctors will be used to solve convection-diffusion equations on parallel computers, with application to aerospace engineering for the solution of Euler equations in computational fluid dynamics simulations. Both theoretical analyses and numerical results demonstrate significant improvement in stability and accuracy by using the new approach.

Original language	American English
Journal	Computers & Mathematics with Applications
Volume	45
DOIs	https://doi.org/10.1016/S0898-1221(03)80013-5
State	Published - Jan 1 2003

Keywords

Time lagging
Explicit predictor
Domain decomposition
Parallel algorithms
Partial differential equations

Disciplines

Applied Mathematics

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10.1016/S0898-1221(03)80013-5License: CC BY

http://dx.doi.org/10.1016/S0898-1221(03)80013-5

Cite this

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title = "An Efficient Parallel Algorithm with Application to Computational Fluid Dynamics",

abstract = " When solving time-dependent partial differential equations on parallel computers using the nonoverlapping domain decomposition method, one often needs numerical boundary conditions on the boundaries between subdomains. These numerical boundary conditions can significantly affect the stability and accuracy of the final algorithm. In this paper, a stability and accuracy analysis of the existing methods for generating numerical boundary conditions will be presented, and a new approach based on explicit predictors and implicit correctors will be used to solve convection-diffusion equations on parallel computers, with application to aerospace engineering for the solution of Euler equations in computational fluid dynamics simulations. Both theoretical analyses and numerical results demonstrate significant improvement in stability and accuracy by using the new approach. ",

keywords = "Time lagging, Explicit predictor, Domain decomposition, Parallel algorithms, Partial differential equations",

author = "W. Rivera and Jianping Zhu and D. Huddleston",

note = "Rivera, W., Zhu, J., and Huddleston, D. (2003). An Efficient parallel algorithm with application to computational fluid dynamics. Computers and Mathematics with Applications, 45(1-3), 165 - 188, doi: 10.1016/S0898-1221(03)80013-5.",

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T1 - An Efficient Parallel Algorithm with Application to Computational Fluid Dynamics

AU - Rivera, W.

AU - Zhu, Jianping

AU - Huddleston, D.

N1 - Rivera, W., Zhu, J., and Huddleston, D. (2003). An Efficient parallel algorithm with application to computational fluid dynamics. Computers and Mathematics with Applications, 45(1-3), 165 - 188, doi: 10.1016/S0898-1221(03)80013-5.

PY - 2003/1/1

Y1 - 2003/1/1

N2 - When solving time-dependent partial differential equations on parallel computers using the nonoverlapping domain decomposition method, one often needs numerical boundary conditions on the boundaries between subdomains. These numerical boundary conditions can significantly affect the stability and accuracy of the final algorithm. In this paper, a stability and accuracy analysis of the existing methods for generating numerical boundary conditions will be presented, and a new approach based on explicit predictors and implicit correctors will be used to solve convection-diffusion equations on parallel computers, with application to aerospace engineering for the solution of Euler equations in computational fluid dynamics simulations. Both theoretical analyses and numerical results demonstrate significant improvement in stability and accuracy by using the new approach.

AB - When solving time-dependent partial differential equations on parallel computers using the nonoverlapping domain decomposition method, one often needs numerical boundary conditions on the boundaries between subdomains. These numerical boundary conditions can significantly affect the stability and accuracy of the final algorithm. In this paper, a stability and accuracy analysis of the existing methods for generating numerical boundary conditions will be presented, and a new approach based on explicit predictors and implicit correctors will be used to solve convection-diffusion equations on parallel computers, with application to aerospace engineering for the solution of Euler equations in computational fluid dynamics simulations. Both theoretical analyses and numerical results demonstrate significant improvement in stability and accuracy by using the new approach.

KW - Time lagging

KW - Explicit predictor

KW - Domain decomposition

KW - Parallel algorithms

KW - Partial differential equations

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/59

UR - http://dx.doi.org/10.1016/S0898-1221(03)80013-5

U2 - 10.1016/S0898-1221(03)80013-5

DO - 10.1016/S0898-1221(03)80013-5

M3 - Article

VL - 45

JO - Computers & Mathematics with Applications

JF - Computers & Mathematics with Applications

ER -

An Efficient Parallel Algorithm with Application to Computational Fluid Dynamics

Abstract

Keywords

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