Well-balanced Preserving of CCWENO-type High Order Entropy Stable Schemes for Shallow Water Equations

doi:10.19596/j.cnki.1001-246x.8744

Abstract

Abstract:

The shallow water equations with source term have steady-state solution. The numerical scheme for solving this kind of equations must have well-balanced property, otherwise it will cause oscillation. For the bottom-non-flat shallow water with source term, this paper studies the well-balanced property of the high order compact central weighted essentially non-oscillatory (CCWENO) entropy stable scheme, and proves its well-balanced property. The theory is verified by one- and two-dimensional numerical examples. The numerical results show that the high order CCWENO scheme has the well-balanced property and can accurately capture the small perturbation of the solution even based on the coarse grid.

Key words: well-balanced, entropy stable scheme, shallow water equations, CCWENO reconstruction, hydrostatic equilibrium state

CLC Number:

O354
O241.82

Shasha LIU, Supei ZHENG, Chengzhi ZHANG, Jianhu FENG. Well-balanced Preserving of CCWENO-type High Order Entropy Stable Schemes for Shallow Water Equations[J]. Chinese Journal of Computational Physics, 2024, 41(4): 453-462.

Figures/Tables 5

Fig.1 Problems of still water with complex bottom

Fig.2 (a) Initial surface level and bottom topography; (b) Results of the three schemes

Fig.3 (a)Initial surface level and bottom topography; (b) Results of the three schemes

Fig.4 Initial surface level and bottom topography; (b) Results of the three schemes

Fig.5 Contours of surface at different times (a) 100 × 50;(b)200 × 100

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