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The shallow-water equations in unidirectional form are also called (de) Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant (see the related section below). The equations are derived [ 2 ] from depth-integrating the Navier–Stokes equations , in the case where the horizontal length scale is much greater than the vertical ...
#!/usr/bin/env python2.7 """ Make an animation of the linear shallow-water equations in 2D Based on the exact solution for axisymmetrical waves in: G. F. Carrier and H. Yeh (2005) Tsunami propagation from a finite source.
It 2D hydrodynamics module, TELEMAC-2D, solves the so-called shallow water equations, also known as the Saint Venant equations. TELEMAC-2D solves the Saint-Venant equations using the finite-element or finite-volume method and a computation mesh of triangular elements. It can perform simulations in transient and permanent conditions. TELEMAC-2D ...
The mathematical model is the 2D shallow water wave equation. As such it cannot resolve vertical convection and consequently not breaking waves or 3D turbulence (e.g. vorticity). All spatial coordinates are assumed to be UTM (meters). As such, ANUGA is unsuitable for modelling flows in areas larger than one and half UTM zones (9 degrees wide).
Adhémar Jean Claude Barré de Saint-Venant (French pronunciation: [ademaʁ ʒɑ̃ klod baʁe də sɛ̃ vənɑ̃]; 23 August 1797 – 6 January 1886) [1] was a mechanician and mathematician who contributed to early stress analysis and also developed the unsteady open channel flow shallow water equations, also known as the Saint-Venant equations that are a fundamental set of equations used in ...
The frictional term in the shallow water equations, is nonlinear in both the velocity and water depth. In order to understand the latter, one can infer from the τ b / ( D 0 + η ) {\displaystyle \tau _{b}/(D_{0}+\eta )} term that the friction is strongest for lower water levels.
Generally speaking, Riemann solvers are specific methods for computing the numerical flux across a discontinuity in the Riemann problem. [1] They form an important part of high-resolution schemes; typically the right and left states for the Riemann problem are calculated using some form of nonlinear reconstruction, such as a flux limiter or a WENO method, and then used as the input for the ...
His later paper in 1940 [5] relaxed this theory from 2D flow to quasi-2D shallow water equations on a beta plane. In this system, the atmosphere is separated into several incompressible layers stacked upon each other, and the vertical velocity can be deduced from integrating the convergence of horizontal flow.