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A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations

Barrenechea, G.R. and Chouly, F. (2009) A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations. Zeitschrift fur Angewandte Mathematik und Mechanik, 89 (1). pp. 54-68. ISSN 0044-2267

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A finite element method to solve the bidimensional Reduced Navier-Stokes Prandtl (RNS/P) equations is described. These equations are an asymptotical simplification of the full Navier-Stokes equations, obtained when one dimension of the domain is of one order smaller than the others. These are therefore of particular interest to describe flows in channels or pipes of small diameter. A low order finite element discretization, based on a piecewise constant approximation of the pressure, is proposed and analyzed. Numerical experiments which consist in fluid flow simulations within a constricted pipe are provided. Comparisons with Navier-Stokes simulations allow to evaluate the performance of prediction of the finite element method, and of the model itself.