Volume 4, Issue 5
A High-Order NVD/TVD-Based Polynomial Upwind Scheme for the Modified Burgers' Equations

Wei Gao ,  Yang Liu ,  Bin Cao and Hong Li

10.4208/aamm.10-m1139

Adv. Appl. Math. Mech., 4 (2012), pp. 617-635.

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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.

  • History

Published online: 2012-04

  • AMS Subject Headings

65M08, 76M12

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