Sur one methode de decentrage de schemas d'elements finis resolvant les equations de Navier-Stokes et de Saint-Venant
Keywords:
finite elements, Navier-Stokes, Shallow-Water equations, , Flux limiting methodsAbstract
A unified finite element method for the computation of two dimensional compressible viscous and free surface flows is presented. The Navier-Stokes (resp. ShallowWater) equations are solved in terms of the dependent variables velocity and cr which is the logarithm of the density (resp. of the head water). It is particulary shown that it is necessary to use stable variational formulation at least for the continuity equation to avoid any oscillations in case of rapid flows. The method proposed herein combines the ideas behind Stream-Line Upwinding Petrov Galerkin Method and Flux limiting methods in order to introduce a stabilisation mechanism only where it is required. Numerical computations of relatively high Reynolds number (2000- 10000) two-dimensional transonic and transcritical flows around a NACA-0012 airfoil exhibit a progression from a steady to periodic vortex sheding flows.
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