TY - JOUR
T1 - Anti-Diffusive Finite Difference WENO Methods for Shallow Water with Transport of Pollutant
AU - Zhengfu Xu & Chi-Wang Shu
JO - Journal of Computational Mathematics
VL - 3
SP - 239
EP - 251
PY - 2006
DA - 2006/06
SN - 24
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8749.html
KW - Anti-diffusive flux correction, Sharpening contact discontinuity, High order accuracy, Finite difference WENO scheme, Saint-Venant system of shallow water, Transport
of pollutant.
AB - <p style="text-align: justify;">In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resolution of contact discontinuities while keeping high order accuracy for the approximation in the smooth region of the solution. The application of the anti-diffusive high order WENO scheme to the Saint-Venant system of shallow water equations with transport of pollutant achieves high resolution. &nbsp;</p>