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

Wei Gao, Yang Liu, Bin Cao & Hong Li

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

Published online: 2012-04

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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

modified Burgers' equation TVD NVD upwind scheme

  • AMS Subject Headings

65M08 76M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-617, author = {Wei Gao, Yang Liu, Bin Cao and Hong Li}, title = {A High-Order NVD/TVD-Based Polynomial Upwind Scheme for the Modified Burgers' Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {5}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1139}, url = {http://global-sci.org/intro/article_detail/aamm/139.html} }
TY - JOUR T1 - A High-Order NVD/TVD-Based Polynomial Upwind Scheme for the Modified Burgers' Equations AU - Wei Gao, Yang Liu, Bin Cao & Hong Li JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 617 EP - 635 PY - 2012 DA - 2012/04 SN - 4 DO - http://dor.org/10.4208/aamm.10-m1139 UR - https://global-sci.org/intro/aamm/139.html KW - modified Burgers' equation KW - TVD KW - NVD KW - upwind scheme AB -

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.

Wei Gao, Yang Liu, Bin Cao & Hong Li. (1970). A High-Order NVD/TVD-Based Polynomial Upwind Scheme for the Modified Burgers' Equations. Advances in Applied Mathematics and Mechanics. 4 (5). 617-635. doi:10.4208/aamm.10-m1139
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