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

A High-Order NVD/TVD-Based Polynomial Upwind Scheme for the Modified Burgers' Equations
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Year:    2012

Author:    Wei Gao, Yang Liu, Bin Cao, Hong Li

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 5 : pp. 617–635

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.10-m1139

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 5 : pp. 617–635

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    modified Burgers' equation TVD NVD upwind scheme.

Author Details

Wei Gao

Yang Liu

Bin Cao

Hong Li

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