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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 ...
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 ...
#!/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.
This equation and notation works in much the same way as the temperature equation. This equation describes the motion of water from one place to another at a point without taking into account water that changes form. Inside a given system, the total change in water with time is zero. However, concentrations are allowed to move with the wind.
The Camassa–Holm equation can be written as the system of equations: [2] + + =, = + + (), with p the (dimensionless) pressure or surface elevation. This shows that the Camassa–Holm equation is a model for shallow water waves with non-hydrostatic pressure and a water layer on a horizontal bed.
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.
What follows is the Richtmyer two-step Lax–Wendroff method. The first step in the Richtmyer two-step Lax–Wendroff method calculates values for f(u(x, t)) at half time steps, t n + 1/2 and half grid points, x i + 1/2.
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.