Peaceman‐Rachford ADI scheme for the two dimensional flow of a second‐grade fluid

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.

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