scholarly journals Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes

2022 ◽  
Vol 7 ◽  
pp. 159-184
Author(s):  
Joao G. Caldas Steinstraesser ◽  
Vincent Guinot ◽  
Antoine Rousseau
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Volumes ◽  
Two Dimensional ◽  
Nonlinear Shallow Water Equations ◽  
Parareal Method

scholarly journals Seiche in the Gulf of Tonkin

1996 ◽  
Vol 18 (1) ◽  
pp. 27-33
Author(s):  
Pham Van Ninh ◽  
Tran Thi Ngoc Duyet
Keyword(s):  
Boundary Condition ◽  
Numerical Modelling ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Forced Oscillation ◽  
Two Dimensional ◽  
Nonlinear Shallow Water Equations ◽  
Liquid Boundary ◽  
Gulf Of Tonkin

Steichen in the Gulf of Tonkin has been studied by numerical modelling based on the two-dimensional nonlinear shallow water equations system with liquid boundary condition given in the form of forced oscillation. The main proper periods have been defined as follows: 23-25 hours, 1-12 hours, 5-7 hours, 2-4 hours. Among them the 23 hours period is the most evident. The obtained results coincide with observed ones at the long shore hydrometeological stations of the Gulf.

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.

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

A shock solution for the nonlinear shallow water equations

2010 ◽  
Vol 658 ◽  
pp. 166-187 ◽  
Author(s):  
MATTEO ANTUONO
Keyword(s):  
Shock Wave ◽  
General Solution ◽  
Theoretical Analysis ◽  
Asymptotic Behaviour ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Boundary Data ◽  
Depth Analysis ◽  
Nonlinear Shallow Water Equations ◽  
Shock Solution

A global shock solution for the nonlinear shallow water equations (NSWEs) is found by assigning proper seaward boundary data that preserve a constant incoming Riemann invariant during the shock wave evolution. The correct shock relations, entropy conditions and asymptotic behaviour near the shoreline are provided along with an in-depth analysis of the main quantities along and behind the bore. The theoretical analysis is then applied to the specific case in which the water at the front of the shock wave is still. A comparison with the Shen & Meyer (J. Fluid Mech., vol. 16, 1963, p. 113) solution reveals that such a solution can be regarded as a specific case of the more general solution proposed here. The results obtained can be regarded as a useful benchmark for numerical solvers based on the NSWEs.

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