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Modifying and Reducing Numerical Dissipation in A Two-Dimensional Central-Upwind Scheme

Published online by Cambridge University Press:  03 June 2015

Chi-Jer Yu and
Chii-Tung Liu
Chi-Jer Yu*
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, 1001 University Road, Hsinchu 300, Taiwan
Chii-Tung Liu
Affiliation:
Department of Computer Science and Information Engineering, Chaoyang University of Technology, 168 Jifong E. Rd., Wufong Township Taichung County 41349, Taiwan
*
Corresponding author. URL:http://www.math.nctu.edu.tw/faculty/e_faculty_content.php?S_ID=31&SC_ID=1, Email: ycj@math.nctu.edu.tw
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Abstract

This study presents a modification of the central-upwind Kurganov scheme for approximating the solution of the 2D Euler equation. The prototype, extended from a 1D model, reduces substantially less dissipation than expected. The problem arises from over-restriction of some slope limiters, which keep slopes between interfaces of cells to be Total-Variation-Diminishing. This study reports the defect and presents a re-derived optimal formula. Numerical experiments highlight the significance of this formula, especially in long-time, large-scale simulations.

Keywords

76T0565M05Hyperbolic systems of conservation lawsGodunov-type finite-volume methodscentral-upwind schemeKurganovnumerical dissipationanti-diffusion

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 3 , June 2012, pp. 340 - 353
Copyright
Copyright © Global-Science Press 2012

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