TY - JOUR
T1 - High Order Well-Balanced Weighted Compact Nonlinear Schemes for Shallow Water Equations
AU - Zhen Gao & Guanghui Hu
JO - Communications in Computational Physics
VL - 4
SP - 1049
EP - 1068
PY - 2017
DA - 2017/10
SN - 22
DO - http://doi.org/10.4208/cicp.OA-2016-0200
UR - https://global-sci.org/intro/article_detail/cicp/9993.html
KW - 
AB - <p style="text-align: justify;">In this study, a numerical framework of the high order well-balanced
weighted compact nonlinear (WCN) schemes is proposed for the shallow water equations
based on the work in [S. Zhang, S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008)
7294-7321]. We employ a special splitting technique for the source term proposed in
[Y. Xing, C.-W Shu, J. Comput. Phys. 208 (2005) 206-227] to maintain the exact C-property,
which can be proved theoretically. In the meantime, the genuine high order
accuracy of the numerical scheme can be observed successfully, and small perturbation
of the stationary state can be resolved and evolved well. In order to capture the
strong discontinuities and large gradients, the fifth-order upwind weighted nonlinear
interpolations together with the fourth/sixth order cell-centered compact scheme are
used to construct different WCN schemes. In addition, the local characteristic projections
are considered to further restrain the potential numerical oscillations. A variety
of representative one- and two-dimensional examples are tested to demonstrate the
good performance of the proposed schemes.</p>