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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 ...
In the mathematical theory of elasticity, Saint-Venant's compatibility condition defines the relationship between the strain and a displacement field by = (+) where ,. Barré de Saint-Venant derived the compatibility condition for an arbitrary symmetric second rank tensor field to be of this form, this has now been generalized to higher rank symmetric tensor fields on spaces of dimension
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 ...
Compatibility conditions are particular cases of integrability conditions and were first derived for linear elasticity by Barré de Saint-Venant in 1864 and proved rigorously by Beltrami in 1886. [1] In the continuum description of a solid body we imagine the body to be composed of a set of infinitesimal volumes or material points.
The original statement was published in French by Saint-Venant in 1855. [2] Although this informal statement of the principle is well known among structural and mechanical engineers, more recent mathematical literature gives a rigorous interpretation in the context of partial differential equations.
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.
With the addition of the three compatibility equations the number of independent equations are reduced to three, matching the number of unknown displacement components. These constraints on the strain tensor were discovered by Saint-Venant, and are called the "Saint Venant compatibility equations".
The momentum equation may be used in situations where the water surface profile is rapidly varied. These situations include hydraulic jumps, hydraulics of bridges, and evaluating profiles at river confluences. For unsteady flow, HEC-RAS solves the full, dynamic, 1-D Saint Venant Equation using an implicit, finite difference method. The unsteady ...