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.

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.

Multilayer shallow water equations with complete Coriolis force. Part 3. Hyperbolicity and stability under shear

2013 ◽  
Vol 723 ◽  
pp. 289-317 ◽  
Author(s):  
Andrew L. Stewart ◽  
Paul J. Dellar
Keyword(s):  
Shallow Water ◽  
Coriolis Force ◽  
Shallow Water Equations ◽  
Three Dimensional ◽  
Direct Calculation ◽  
Shear Instability ◽  
Vertical Shear ◽  
Vortex Sheets ◽  
Multilayer Shallow Water Equations ◽  
Complete Coriolis Force

AbstractWe analyse the hyperbolicity of our multilayer shallow water equations that include the complete Coriolis force due to the Earth’s rotation. Shallow water theory represents flows in which the vertical shear is concentrated into vortex sheets between layers of uniform velocity. Such configurations are subject to Kelvin–Helmholtz instabilities, with arbitrarily large growth rates for sufficiently short-wavelength disturbances. These instabilities manifest themselves through a loss of hyperbolicity in the shallow water equations, rendering them ill-posed for the solution of initial value problems. We show that, in the limit of vanishingly small density difference between the two layers, our two-layer shallow water equations remain hyperbolic when the velocity difference remains below the same threshold that also ensures the hyperbolicity of the standard shallow water equations. Direct calculation of the domain of hyperbolicity becomes much less tractable for three or more layers, so we demonstrate numerically that the threshold for the velocity differences, below which the three-layer equations remain hyperbolic, is also unchanged by the inclusion of the complete Coriolis force. In all cases, the shape of the domain of hyperbolicity, which extends outside the threshold, changes considerably. The standard shallow water equations only lose hyperbolicity due to shear parallel to the direction of wave propagation, but the complete Coriolis force introduces another mechanism for loss of hyperbolicity due to shear in the perpendicular direction. We demonstrate that this additional mechanism corresponds to the onset of a transverse shear instability driven by the non-traditional components of the Coriolis force in a three-dimensional continuously stratified fluid.

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.

scholarly journals Numerical approximation of the shallow water equations with coriolis source term

2021 ◽  
Vol 70 ◽  
pp. 31-44
Author(s):  
E. Audusse ◽  
V. Dubos ◽  
A. Duran ◽  
N. Gaveau ◽  
Y. Nasseri ◽  
...  
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Coriolis Force ◽  
Shallow Water Equations ◽  
Numerical Approximation ◽  
Energy Estimates ◽  
Discrete Energy ◽  
Geostrophic Balance ◽  
Low Froude Number ◽  
Numerical Fluxes

We investigate in this work a class of numerical schemes dedicated to the non-linear Shallow Water equations with topography and Coriolis force. The proposed algorithms rely on Finite Volume approximations formulated on collocated and staggered meshes, involving appropriate diffusion terms in the numerical fluxes, expressed as discrete versions of the linear geostrophic balance. It follows that, contrary to standard Finite-Volume approaches, the linear versions of the proposed schemes provide a relevant approximation of the geostrophic equilibrium. We also show that the resulting methods ensure semi-discrete energy estimates. Numerical experiments exhibit the efficiency of the approach in the presence of Coriolis force close to the geostrophic balance, especially at low Froude number regimes.

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