The Wave Equation Applied To The Solution Of Navier-Stokes Equations In Finite Elements
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J.-M. Hervouet & E. Razafindrakoto
This paper deals with the numerical solution of 3-dimensional Navier-Stokes equations with a free surface, in the framework of finite elements and the Telemac system. The idea of the wave equation is applied here. It was previously used for solving Shallow Water Equations and consists of eliminating the velocity in the depth-averaged continuity equation thanks to an expression obtained with the momentum equations. After an overview of the basic solution procedure in Telemac-3D we detail the new algorithm and show its advantages in terms of computer time. Keywords: wave equation, pseudo-wave equation, Navier-Stokes equations, finite elements, Telemac system. 1 Introduction The hydroinformatic system Telemac, based on Finite Element techniques, addresses free surface and underground flows. In its present development stage, the system includes the Saint-Venant or shallow water equations (Telemac-2D), Navier-Stokes equations in 3 dimensions with a free surface (Telemac-3D), and also mild slope equations, wave action equations, water quality models, sediment transport equations in 2D and 3D, Richard's equations in 2D and 3D. Recent advances have led to a robust algorithm for the treatment of full non-hydrostatic 3D Navier-Stokes equations with a free surface, which allows rapid flows, hydraulic jumps, wetting and drying, so that computations of a dam-break flood waves can now be performed (see ref. ). The solution procedure in Telemac-3D is based upon a fractional step approach and, in previous versions, one of the steps was a solution of Shallow
wave equation, pseudo-wave equation, Navier-Stokes equations, finite elements, Telemac system.