scholarly journals A numerical method for the two layer shallow water equations with dry states

2013 ◽  
Vol 72 ◽  
pp. 80-91 ◽  
Author(s):  
Kyle T. Mandli
Keyword(s):  
Shallow Water ◽  
Numerical Method ◽  
Shallow Water Equations

Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

2014 ◽  
Vol 16 (5) ◽  
pp. 1323-1354 ◽  
Author(s):  
Manuel Jesús Castro Diaz ◽  
Yuanzhen Cheng ◽  
Alina Chertock ◽  
Alexander Kurganov
Keyword(s):  
Shallow Water ◽  
Numerical Method ◽  
Shallow Water Equations ◽  
Numerical Experiments ◽  
Operator Splitting ◽  
Finite Volume Methods ◽  
Splitting Methods ◽  
Upwind Scheme ◽  
Operator Splitting Methods ◽  
Numerical Approaches

AbstractIn this paper, we develop and study numerical methods for the two-mode shallow water equations recently proposed in [S. STECHMANN, A. MAJDA, and B. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407-432]. Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms. We present several numerical approaches—two operator splitting methods (based on either Roe-type upwind or central-upwind scheme), a central-upwind scheme and a path-conservative central-upwind scheme—and test their performance in a number of numerical experiments. The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method.

scholarly journals Construction, verification of a software for the 2D dam-break flow and some its applications

2007 ◽  
Vol 29 (4) ◽  
pp. 539-550
Author(s):  
Hoang Van Lai ◽  
Nguyen Thanh Don
Keyword(s):  
Shallow Water ◽  
Numerical Method ◽  
Shallow Water Equations ◽  
Theoretical Basis ◽  
Dam Break ◽  
River Delta ◽  
Red River ◽  
Test Cases ◽  
Red River Delta ◽  
Dam Break Flow

In this paper the numerical method for the shallow water equations is studied. The paper consists of 3 sections. In the section 1 the theoretical basis and software IMECI-L2DBREAK for simulation of the 2D dam-break or dyke-break flows is outlined. In the section 2 some results in verification of the IMECH_2DBREAK by the test cases proposed in the big European Hydraulics Laboratories are shown. In the last section some applications of IMECH_2DBREAK for the inundation problem in the Red river delta in the Northern of Vietnam are presented.

Modelling the Azov Sea circulation and extreme surges in 2013-2014 using the regularized shallow water equations

2018 ◽  
Vol 33 (3) ◽  
pp. 173-185 ◽  
Author(s):  
Dmitry S. Saburin ◽  
Tatiana G. Elizarova
Keyword(s):  
Shallow Water ◽  
Numerical Method ◽  
Coriolis Force ◽  
Shallow Water Equations ◽  
Numerical Algorithms ◽  
Water Area ◽  
Observation Data ◽  
Wind Effects ◽  
New Model ◽  
Azov Sea

Abstract A new model for calculation of circulation in shallow water basins is created based on the shallow water equations taking into account the Coriolis force and quadratic friction on the bottom. Wind effects are taken into account as forcing. The main feature of the model is a new numerical method based on regularized shallow water equations allowing one to construct the simple and sufficiently accurate numerical algorithms possessing a number of advantages over existing methods. The paper provides a detailed description of all construction steps of the model. The developed model was implemented for the water area of the Azov Sea. The paper presents the modelling of extreme surges in March 2013 and September 2014, the results of calculations are compared with observation data of hydrometeorological stations in Taganrog and Yeysk.

scholarly journals NUMERICAL METHOD FOR 1-D SHALLOW WATER EQUATIONS BASED ON FLUX DIFFERENCE SPLITTING

2000 ◽  
Vol 44 ◽  
pp. 473-478
Author(s):  
Juichiro AKIYAMA ◽  
Masaru URA ◽  
Mirei SHIGEEDA ◽  
Akhilesh Kumar JHA
Keyword(s):  
Shallow Water ◽  
Numerical Method ◽  
Shallow Water Equations ◽  
Flux Difference

MAPPING TIDAL CURRENTS AND RESIDUAL CURRENTS BY USE OF COASTAL ACOUSTIC TOMOGRAPHY

2017 ◽  
Author(s):  
Xiao-Hua Zhu ◽  
Xiao-Hua Zhu ◽  
Ze-Nan Zhu ◽  
Ze-Nan Zhu ◽  
Xinyu Guo ◽  
...  
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Mean Amplitude ◽  
Momentum Equation ◽  
Tidal Currents ◽  
Acoustic Tomography ◽  
Mean Values ◽  
Residual Currents ◽  
Water Depths ◽  
Deep Area

A coastal acoustic tomography (CAT) experiment for mapping the tidal currents in the Zhitouyang Bay was successfully carried out with seven acoustic stations during July 12 to 13, 2009. The horizontal distributions of tidal current in the tomography domain are calculated by the inverse analysis in which the travel time differences for sound traveling reciprocally are used as data. Spatial mean amplitude ratios M2 : M4 : M6 are 1.00 : 0.15 : 0.11. The shallow-water equations are used to analyze the generation mechanisms of M4 and M6. In the deep area, velocity amplitudes of M4 measured by CAT agree well with those of M4 predicted by the advection terms in the shallow water equations, indicating that M4 in the deep area where water depths are larger than 60 m is predominantly generated by the advection terms. M6 measured by CAT and M6 predicted by the nonlinear quadratic bottom friction terms agree well in the area where water depths are less than 20 m, indicating that friction mechanisms are predominant for generating M6 in the shallow area. Dynamic analysis of the residual currents using the tidally averaged momentum equation shows that spatial mean values of the horizontal pressure gradient due to residual sea level and of the advection of residual currents together contribute about 75% of the spatial mean values of the advection by the tidal currents, indicating that residual currents in this bay are induced mainly by the nonlinear effects of tidal currents.

Sign in / Sign up

Export Citation Format

Share Document