The Library
Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes
Tools
Duque-Daza, Carlos, Lockerby, Duncan A. and Galeano, Carlos (2011) Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes. Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol.33 (No.4). pp. 381-392. doi:10.1590/S1678-58782011000400001 ISSN 1678-5878.
|
Text
WRAP_Lockerby_a01v33n4.pdf - Published Version Download (1151Kb) | Preview |
Official URL: http://dx.doi.org/10.1590/S1678-58782011000400001
Abstract
We present a computational study of the solution of the Falkner-Skan equation (a third-order boundary value problem arising in boundary-layer theory) using high-order and high-order-compact finite differences schemes. There are a number of previously reported solution approaches that adopt a reduced-order system of equations, and numerical methods such as: shooting, Taylor series, Runge-Kutta and other semi-analytic methods. Interestingly, though, methods that solve the original non-reduced third-order equation directly are absent from the literature. Two high-order schemes are presented using both explicit (third-order) and implicit compact-difference (fourth-order) formulations on a semi-infinite domain; to our knowledge this is the first time that high-order finite difference schemes are presented to find numerical solutions to the non-reduced-order Falkner-Skan equation directly. This approach maintains the simplicity of Taylor-series coefficient matching methods, avoiding complicated numerical algorithms, and in turn presents valuable information about the numerical behaviour of the equation. The accuracy and effectiveness of this approach is established by comparison with published data for accelerating, constant and decelerating flows; excellent agreement is observed. In general, the numerical behaviour of formulations that seek an optimum physical domain size (for a given computational grid) is discussed. Based on new insight into such methods, an alternative optimisation procedure is proposed that should increase the range of initial seed points for which convergence can be achieved.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics T Technology > T Technology (General) |
||||
Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||
Library of Congress Subject Headings (LCSH): | Laminar boundary layer, Finite differences, Similarity (Geometry) | ||||
Journal or Publication Title: | Journal of the Brazilian Society of Mechanical Sciences and Engineering | ||||
Publisher: | Brazilian Society of Mechanical Sciences and Engineering | ||||
ISSN: | 1678-5878 | ||||
Official Date: | October 2011 | ||||
Dates: |
|
||||
Volume: | Vol.33 | ||||
Number: | No.4 | ||||
Page Range: | pp. 381-392 | ||||
DOI: | 10.1590/S1678-58782011000400001 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 19 December 2015 | ||||
Date of first compliant Open Access: | 19 December 2015 |
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year