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A multilayer Saint-Venant model: Derivation and numerical validation
We introduce a new variant of the multilayer Saint-Venant system. The classical Saint-Venant system is a well-known approximation of the
incompressible Navier-Stokes equations for shallow water flows with free moving boundary. Its efficiency, robustness and low computational cost make it
very commonly used. Nevertheless its range of application is limited and it
does not allow to access to the vertical profile of the horizontal velocity. Hence
and thanks to a precise analysis of the shallow water assumption we propose
here a new approximation of the Navier-Stokes equations which consists in a
set of coupled Saint-Venant systems, extends the range of validity and gives a
precise description of the vertical profile of the horizontal velocity while preserving the computational efficiency of the classical Saint-Venant system. We
validate the model through some numerical examples.