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.
| Original language | English |
|---|---|
| Pages (from-to) | 228-242 |
| Number of pages | 15 |
| Journal | International Journal of Numerical Methods for Heat and Fluid Flow |
| Volume | 22 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2012 |
| Externally published | Yes |
Keywords
- ADI
- Cattanneo equation
- Crank-Nicolson
- Second-grade fluid
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics