TY - JOUR
T1 - Simulations of Shallow Water Equations by Finite Difference WENO Schemes with Multilevel Time Discretization
AU - Changna Lu & Gang Li
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 505
EP - 524
PY - 2011
DA - 2011/04
SN - 4
DO - http://doi.org/10.4208/nmtma.2011.m1027
UR - https://global-sci.org/intro/article_detail/nmtma/5981.html
KW - Multilevel time discretization, weighted essentially non-oscillatory schemes, shallow
water equations, Runge-Kutta method, high order accuracy.
AB - <p style="text-align: justify;">In this paper we study a class of multilevel high order time
discretization procedures for the finite difference weighted
essential non-oscillatory (WENO) schemes to solve the
one-dimensional and two-dimensional shallow water equations with
source terms. Multilevel time discretization methods can make full
use of computed information by WENO spatial discretization and save
CPU cost by holding the former computational values. Extensive
simulations are performed, which indicate that, the finite difference WENO
schemes with multilevel time discretization can achieve higher accuracy,
and are more cost effective than WENO
scheme with Runge-Kutta time discretization, while still maintaining nonoscillatory properties.</p>