TY - JOUR
T1 - A High-Order NVD/TVD-Based Polynomial Upwind Scheme for the Modified Burgers' Equations
AU - Gao , Wei
AU - Liu , Yang
AU - Cao , Bin
AU - Li , Hong
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 617
EP - 635
PY - 2012
DA - 2012/04
SN - 4
DO - http://doi.org/10.4208/aamm.10-m1139
UR - https://global-sci.org/intro/article_detail/aamm/139.html
KW - modified Burgers' equation, TVD, NVD, upwind scheme.
AB - <p style="text-align: justify;">A bounded high order upwind scheme is presented for the modified Burgers&#39; 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&#39; equation.</p>