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

被引：7

作者：

Momoniat, E. ^{[1
]}

Harley, C. ^{[1
]}

机构：

[1] Univ Witwatersrand, Sch Computat & Appl Math, Ctr Differential Equat Continuum Mech & Applicat, Johannesburg, South Africa

来源：

INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW | 2012年 / 22卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Second-grade fluid; Cattanneo equation; Crank-Nicolson; ADI; DIFFUSION; EQUATIONS; CONVERGENCE; STABILITY;

D O I：

10.1108/09615531211199845

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

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.

引用

页码：228 / 242

页数：15

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