Title: Overshoot/Undershoot behaviour predicted by some high-resolution composite schemes following G/L CBC

Authors: Jin-Jia Wei, Bo Yu, Wen-Quan Tao, Yasuo Kawaguchi

Addresses: State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China. ' Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum (Beijing), Beijing 102249, People's Republic of China. ' State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China. E-mail: wqtao@mail.xjtu.edu.cn ' Faculty of Science and Technology, Department of Mechanical Engineering, Tokyo University of Science, Noda 278-8510, Japan

Abstract: Analysis of a discretised scalar equation shows that high-resolution composite schemes containing a characteristic line of ˆφf = 1 on the Normalised Variable Diagram (NVD), although following the Convective Boundedness Criterion (CBC) proposed by Gaskell and Lau, may result in numerical results dependent on initial field, and thus may predict overshoot/undershoot behaviour. The finding is confirmed by testing a case of pure convection of a double-step profile in an oblique uniform velocity field. A slightly revised CBC is proposed by excluding the line of ˆφf = 1 from the CBC region, and can predict bounded numerical results without losing accuracy.

Keywords: high-resolution composite schemes; convective boundedness criterion; overshoot-undershoot; revised CBC; discretised scalar equations; pure convection; double-step profile; oblique uniform velocity.

DOI: 10.1504/PCFD.2009.024829

Progress in Computational Fluid Dynamics, An International Journal, 2009 Vol.9 No.3/4/5, pp.277 - 282

Published online: 01 May 2009 *

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