Peaceman‐Rachford ADI scheme for the two dimensional flow of a second‐grade fluid
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 23 March 2012
Abstract
Purpose
The purpose of this paper is to obtain numerical solutions of a two‐dimensional mixed space‐time PDE modelling the flow of a second‐grade.
Design/methodology/approach
The paper derives conditionally stable Crank‐Nicolson schemes to solve both the one and two dimensional mixed‐space time PDE. For the two‐dimensional case we implement the Crank‐Nicolson scheme using a Peaceman‐Rachford ADI scheme.
Findings
For zero‐shear boundaries the Cattanneo representation of the model equation blows up whilst the representation derived by Rajagopal is stable and produces solutions which decay over time.
Originality/value
The use of a Peaceman‐Rachford ADI scheme to solve a mixed space‐time PDE is both novel and new.
Keywords
Citation
Momoniat, E. and Harley, C. (2012), "Peaceman‐Rachford ADI scheme for the two dimensional flow of a second‐grade fluid", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 2, pp. 228-242. https://doi.org/10.1108/09615531211199845
Publisher
:Emerald Group Publishing Limited
Copyright © 2012, Emerald Group Publishing Limited