TY - JOUR
T1 - A Positivity-Preserving and Well-Balanced High Order Compact Finite Difference Scheme for Shallow Water Equations
AU - Ren , Baifen
AU - Gao , Zhen
AU - Gu , Yaguang
AU - Xie , Shusen
AU - Zhang , Xiangxiong
JO - Communications in Computational Physics
VL - 2
SP - 524
EP - 552
PY - 2024
DA - 2024/03
SN - 35
DO - http://doi.org/10.4208/cicp.OA-2023-0034
UR - https://global-sci.org/intro/article_detail/cicp/22981.html
KW - Well-balanced, positivity-preserving, compact finite difference.
AB - <p style="text-align: justify;">We construct a positivity-preserving and well-balanced high order accurate
finite difference scheme for solving shallow water equations under the fourth order
compact finite difference framework. The source term is rewritten to balance the flux
gradient in steady state solutions. Under a suitable CFL condition, the proposed compact difference scheme satisfies weak monotonicity, i.e., the average water height defined by the weighted average of a three-points stencil stays non-negative in forward
Euler time discretization. Thus, a positivity-preserving limiter can be used to enforce
the positivity of water height point values in a high order strong stability preserving Runge-Kutta method. A TVB limiter for compact finite difference scheme is also
used to reduce numerical oscillations, without affecting well-balancedness and positivity. Numerical experiments verify that the proposed scheme is high-order accurate,
positivity-preserving, well-balanced and free of numerical oscillations.</p>