Cover Image

Application Of Higher Order Compact Finite Difference Methods To Problems In Fluid Dynamics

Finite difference schemes used in the field of computational fluid dynamics is generally only of second-order accurate in representing the spatial derivatives. Numerical algorithms based on higher order finite difference schemes that can achieve fourth-order accuracy in space have been developed....

Full description

Saved in:
Bibliographic Details
Main Author: Yap, Wen Jiun
Format: Thesis
Language:English
English
Published: 2003
Subjects:
Finite differences
Fluid dynamics - Problems
Online Access:http://psasir.upm.edu.my/id/eprint/12188/1/FK_2003_38_.pdf
http://psasir.upm.edu.my/id/eprint/12188/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.upm.eprints.12188
record_format eprints
spelling my.upm.eprints.121882024-07-04T02:57:24Z http://psasir.upm.edu.my/id/eprint/12188/ Application Of Higher Order Compact Finite Difference Methods To Problems In Fluid Dynamics Yap, Wen Jiun Finite difference schemes used in the field of computational fluid dynamics is generally only of second-order accurate in representing the spatial derivatives. Numerical algorithms based on higher order finite difference schemes that can achieve fourth-order accuracy in space have been developed. Higher order schemes will enable a larger grid size with fewer grid points to sufficiently give fine results. A compact scheme, which preserves the smaller stencil size, is preferred due to its simplicity and computational efficiency, as opposed to the normal approach to expand the stencil to achieve higher accuracy. Two approaches are used to obtain the fourth-order accurate compact scheme. In Lax-Wendroff approach, the governing differential equations are used to approximate the leading truncation error in the second-order central difference of the governing equations. In Hermitian scheme, the fourth-order approximations to the derivatives are treated as unknowns. These unknowns are solved explicitly with Hermitian relations that relate the variables and its spatial derivatives. The numerical algorithms are first developed for viscous Burgers' equation on uniform and clustered grids. The fourth-order accuracy and convergence rate is demonstrated. The performance of the two different approaches are compared and found on par with each other. Second, the numerical algorithms are used to solve the quasi-one-dimensional subsonic-supersonic nozzle flow. The Hermitian scheme shows excellent agreement with the analytical result but the Lax-Wendroff approach failed to do so due to instability problem. Third, only the numerical algorithm based on Hermitian scheme is used to solve the flow past a backward-facing step. The reattachment lengths of the first separation bubble compare favourably with previously published results in the literature. The success of the fourth-order compact finite difference schemes in solving the viscous Burgers' equation is not repeated in the isentropic nozzle flow and the flow past a backward-facing step. Further efforts have to be made to improve the convergence rate of the numerical solution of the isentropic nozzle flow using the Hermitian scheme and to overcome the instability in the numerical solution of the same problem using the Lax-Wendroff approach. 2003-02 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/12188/1/FK_2003_38_.pdf Yap, Wen Jiun (2003) Application Of Higher Order Compact Finite Difference Methods To Problems In Fluid Dynamics. Masters thesis, Universiti Putra Malaysia. Finite differences Fluid dynamics - Problems English
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
English
topic Finite differences
Fluid dynamics - Problems
spellingShingle Finite differences
Fluid dynamics - Problems
Yap, Wen Jiun
Application Of Higher Order Compact Finite Difference Methods To Problems In Fluid Dynamics
description Finite difference schemes used in the field of computational fluid dynamics is generally only of second-order accurate in representing the spatial derivatives. Numerical algorithms based on higher order finite difference schemes that can achieve fourth-order accuracy in space have been developed. Higher order schemes will enable a larger grid size with fewer grid points to sufficiently give fine results. A compact scheme, which preserves the smaller stencil size, is preferred due to its simplicity and computational efficiency, as opposed to the normal approach to expand the stencil to achieve higher accuracy. Two approaches are used to obtain the fourth-order accurate compact scheme. In Lax-Wendroff approach, the governing differential equations are used to approximate the leading truncation error in the second-order central difference of the governing equations. In Hermitian scheme, the fourth-order approximations to the derivatives are treated as unknowns. These unknowns are solved explicitly with Hermitian relations that relate the variables and its spatial derivatives. The numerical algorithms are first developed for viscous Burgers' equation on uniform and clustered grids. The fourth-order accuracy and convergence rate is demonstrated. The performance of the two different approaches are compared and found on par with each other. Second, the numerical algorithms are used to solve the quasi-one-dimensional subsonic-supersonic nozzle flow. The Hermitian scheme shows excellent agreement with the analytical result but the Lax-Wendroff approach failed to do so due to instability problem. Third, only the numerical algorithm based on Hermitian scheme is used to solve the flow past a backward-facing step. The reattachment lengths of the first separation bubble compare favourably with previously published results in the literature. The success of the fourth-order compact finite difference schemes in solving the viscous Burgers' equation is not repeated in the isentropic nozzle flow and the flow past a backward-facing step. Further efforts have to be made to improve the convergence rate of the numerical solution of the isentropic nozzle flow using the Hermitian scheme and to overcome the instability in the numerical solution of the same problem using the Lax-Wendroff approach.
format Thesis
author Yap, Wen Jiun
author_facet Yap, Wen Jiun
author_sort Yap, Wen Jiun
title Application Of Higher Order Compact Finite Difference Methods To Problems In Fluid Dynamics
title_short Application Of Higher Order Compact Finite Difference Methods To Problems In Fluid Dynamics
title_full Application Of Higher Order Compact Finite Difference Methods To Problems In Fluid Dynamics
title_fullStr Application Of Higher Order Compact Finite Difference Methods To Problems In Fluid Dynamics
title_full_unstemmed Application Of Higher Order Compact Finite Difference Methods To Problems In Fluid Dynamics
title_sort application of higher order compact finite difference methods to problems in fluid dynamics
publishDate 2003
url http://psasir.upm.edu.my/id/eprint/12188/1/FK_2003_38_.pdf
http://psasir.upm.edu.my/id/eprint/12188/
_version_ 1804067020781649920
score 13.211869

Similar Items