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A High-Order NVD/TVD-Based Polynomial Upwind Scheme for the Modified Burgers’ Equations

Published online by Cambridge University Press:  03 June 2015

Wei Gao ,
Yang Liu ,
Bin Cao  and
Hong Li
Wei Gao*
Affiliation:
School of Mathematical Sciences, Inner Mongolia University, Huhhot, P. R. China
Yang Liu*
Affiliation:
School of Mathematical Sciences, Inner Mongolia University, Huhhot, P. R. China
Bin Cao*
Affiliation:
School of Mathematical Sciences, Inner Mongolia University, Huhhot, P. R. China
Hong Li*
Affiliation:
School of Mathematical Sciences, Inner Mongolia University, Huhhot, P. R. China
*
Corresponding author. Email: mathgao@mail.ustc.edu.cn
Email: mathliuyang@yahoo.cn
Email: bincao@gmail.com
Email: smslh@imu.edu.cn
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Abstract

A bounded high order upwind scheme is presented for the modified Burgers’ equation by using the normalized-variable formulation in the finite volume framework. The characteristic line of the present scheme in the normalized-variable diagram is designed on the Hermite polynomial interpolation. In order to suppress unphysical oscillations, the present scheme respects both the TVD (total variational diminishing) constraint and CBC (convection boundedness criterion) condition. Numerical results demonstrate the present scheme possesses good robustness and high resolution for the modified Burgers’ equation.

Keywords

65M0876M12modified Burgers’ equationTVDNVDupwind scheme

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Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 5 , October 2012 , pp. 617 - 635
Copyright
Copyright © Global-Science Press 2012

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