An Energy-Stable High-Order Central Difference Scheme for the Two-Dimensional Shallow Water Equations

2005 ◽  
Vol 28 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Matthew Brown ◽  
Margot Gerritsen
Keyword(s):  
Difference Scheme ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
High Order ◽  
Two Dimensional ◽  
Central Difference ◽  
Central Difference Scheme ◽  
Energy Stable

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

High Order Two Dimensional Numerical Schemes for the Coupling of Transport Equations and Shallow Water Equations

2008 ◽  
pp. 241-248
Author(s):  
M. J. Castro ◽  
E. D. Fernández Nieto ◽  
A. M. Ferreiro Ferreiro ◽  
J. A. García Rodríguez ◽  
C. Parés
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Transport Equations ◽  
High Order ◽  
Two Dimensional ◽  
Numerical Schemes

A Semi-Implicit Runge–Kutta Time-Difference Scheme for the Two-Dimensional Shallow-Water Equations

2006 ◽  
Vol 134 (10) ◽  
pp. 2916-2926 ◽  
Author(s):  
Sajal K. Kar
Keyword(s):  
Difference Scheme ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Time Difference ◽  
Water Model ◽  
Two Dimensional ◽  
Runge Kutta ◽  
Initial Boundary Value

Abstract A semi-implicit, two time-level, three-step iterative time-difference scheme is proposed for the two-dimensional nonlinear shallow-water equations in a conservative flux form. After a semi-implicit linearization of the governing equations, the linear gravity wave terms are time discretized implicitly using a second-order trapezoidal scheme applied over each iterative step, whereas the nonlinear terms including horizontal advection and other terms left over from the semi-implicit linearization are time discretized explicitly using a third-order Runge–Kutta scheme. The effectiveness of the scheme in terms of numerical accuracy, stability, and efficiency is established through a forced initial-boundary value problem studied using a two-dimensional shallow-water model.

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

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