A variational approach to the derivation of high-order shallow-water equations

1994 ◽  
Vol 17 (2) ◽  
pp. 175-189 ◽  
Author(s):  
F. Mattioli
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Variational Approach ◽  
High Order

scholarly journals A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction

2021 ◽  
pp. 105152
Author(s):  
Victor Michel-Dansac ◽  
Christophe Berthon ◽  
Stéphane Clain ◽  
Françoise Foucher
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
High Order ◽  
Two Dimensional

Fast and high-order solutions to the spherical shallow water equations

2000 ◽  
Vol 33 (1-4) ◽  
pp. 191-197
Author(s):  
William F. Spotz ◽  
Mark A. Taylor ◽  
Paul N. Swarztrauber
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
High Order

High Order Well-Balanced Weighted Compact Nonlinear Schemes for Shallow Water Equations

2017 ◽  
Vol 22 (4) ◽  
pp. 1049-1068 ◽  
Author(s):  
Zhen Gao ◽  
Guanghui Hu
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
High Order ◽  
High Order Accuracy ◽  
Local Characteristic ◽  
Order Accuracy ◽  
Splitting Technique ◽  
Strong Discontinuities ◽  
Comput Phys ◽  
Fifth Order

AbstractIn 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.

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