An adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations

Ghazizadeh，Mohammad A.1; Mohammadian，Abdolmajid1; Kurganov，Alexander2

2020-08-15

10.1016/j.compfluid.2020.104633

COMPUTERS & FLUIDS   影响因子和分区

0045-7930

1879-0747

We present an adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations. The use of quadtree grids results in a robust, efficient and highly accurate numerical method. The quadtree model is developed based on the well-balanced positivity preserving central-upwind scheme proposed in [A. KURGANOV AND G. PETROVA, Commun. Math. Sci., 5 (2007), pp. 133–160]. The designed scheme is well-balanced in the sense that it is capable of exactly preserving “lake-at-rest” steady states. In order to achieve this as well as to preserve positivity of water depth, a continuous piecewise bilinear interpolation of the bottom topography function is utilized. This makes the proposed scheme capable of modelling flows over discontinuous bottom topography. Local gradients are examined to determine new seeding points in grid refinement for the next timestep. Numerical examples demonstrate the promising performance of the central-upwind quadtree scheme.

Central-upwind scheme Positivity preserving scheme Quadtree grids Shallow water equations Well-balanced scheme

SCI ; EI

英语

其他

NSERC[210717] ; NSFC[11771201] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001]

Computer Science ; Mechanics

Computer Science, Interdisciplinary Applications ; Mechanics

WOS:000563869900016

PERGAMON-ELSEVIER SCIENCE LTD

20202608879197

Topography ; Equations of motion

Calculus:921.2 ; Numerical Methods:921.6 ; Materials Science:951

COMPUTER SCIENCE

2-s2.0-85086892954

Scopus

1.Department of Civil Engineering,University of Ottawa,Ottawa,K1N 6N5,Canada
2.Department of Mathematics and SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,518055,China

Ghazizadeh，Mohammad A.,Mohammadian，Abdolmajid,Kurganov，Alexander. An adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations[J]. COMPUTERS & FLUIDS,2020,208.

Ghazizadeh，Mohammad A.,Mohammadian，Abdolmajid,&Kurganov，Alexander.(2020).An adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations.COMPUTERS & FLUIDS,208.

Ghazizadeh，Mohammad A.,et al."An adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations".COMPUTERS & FLUIDS 208(2020).