Adaptive grid refinement using the generalized finite difference method

Paul Kew

Research output: ThesisDoctoral Thesis

Abstract

The combination of the GFDM, and adaptive grid refinement is applied to solve 2D fluid flow problems. The accuracy of this combination is demonstrated by solving the 2D lid-driven cavity flow, and 2D backward-facing step flow problems, and comparing the results against the benchmarks. This new CFD formulation is applied to solve a 2D meter flow application to determine the velocity profiles through the centre of the meter for higher Reynolds numbers.

To verify the accuracy of this combination, analytical 2D and 3D Laplace PDE’s are solved by two methods. The first method uses the FDM over a uniform grid of nodes, and the second method uses the GFDM over a non-uniform grid of nodes. Program speed and accuracy comparisons are made for both methods.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Charles Sturt University
Supervisors/Advisors
  • Li, Jan, Principal Supervisor
  • Kemp, Michael, Co-Supervisor
  • Charlton, Philip, Co-Supervisor
Place of PublicationAustralia
Publisher
Publication statusPublished - 20 Nov 2019

Fingerprint

Finite difference method
Frequency division multiplexing
Flow of fluids
Computational fluid dynamics
Reynolds number

Cite this

Kew, P. (2019). Adaptive grid refinement using the generalized finite difference method. Australia: Charles Sturt University.
Kew, Paul. / Adaptive grid refinement using the generalized finite difference method. Australia : Charles Sturt University, 2019. 169 p.
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abstract = "The combination of the GFDM, and adaptive grid refinement is applied to solve 2D fluid flow problems. The accuracy of this combination is demonstrated by solving the 2D lid-driven cavity flow, and 2D backward-facing step flow problems, and comparing the results against the benchmarks. This new CFD formulation is applied to solve a 2D meter flow application to determine the velocity profiles through the centre of the meter for higher Reynolds numbers.To verify the accuracy of this combination, analytical 2D and 3D Laplace PDE’s are solved by two methods. The first method uses the FDM over a uniform grid of nodes, and the second method uses the GFDM over a non-uniform grid of nodes. Program speed and accuracy comparisons are made for both methods.",
author = "Paul Kew",
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Kew, P 2019, 'Adaptive grid refinement using the generalized finite difference method', Doctor of Philosophy, Charles Sturt University, Australia.

Adaptive grid refinement using the generalized finite difference method. / Kew, Paul.

Australia : Charles Sturt University, 2019. 169 p.

Research output: ThesisDoctoral Thesis

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T1 - Adaptive grid refinement using the generalized finite difference method

AU - Kew, Paul

PY - 2019/11/20

Y1 - 2019/11/20

N2 - The combination of the GFDM, and adaptive grid refinement is applied to solve 2D fluid flow problems. The accuracy of this combination is demonstrated by solving the 2D lid-driven cavity flow, and 2D backward-facing step flow problems, and comparing the results against the benchmarks. This new CFD formulation is applied to solve a 2D meter flow application to determine the velocity profiles through the centre of the meter for higher Reynolds numbers.To verify the accuracy of this combination, analytical 2D and 3D Laplace PDE’s are solved by two methods. The first method uses the FDM over a uniform grid of nodes, and the second method uses the GFDM over a non-uniform grid of nodes. Program speed and accuracy comparisons are made for both methods.

AB - The combination of the GFDM, and adaptive grid refinement is applied to solve 2D fluid flow problems. The accuracy of this combination is demonstrated by solving the 2D lid-driven cavity flow, and 2D backward-facing step flow problems, and comparing the results against the benchmarks. This new CFD formulation is applied to solve a 2D meter flow application to determine the velocity profiles through the centre of the meter for higher Reynolds numbers.To verify the accuracy of this combination, analytical 2D and 3D Laplace PDE’s are solved by two methods. The first method uses the FDM over a uniform grid of nodes, and the second method uses the GFDM over a non-uniform grid of nodes. Program speed and accuracy comparisons are made for both methods.

M3 - Doctoral Thesis

PB - Charles Sturt University

CY - Australia

ER -

Kew P. Adaptive grid refinement using the generalized finite difference method. Australia: Charles Sturt University, 2019. 169 p.