Application de Ia methode des elements finis aux equations 2-D hyperboliques. Partie I : equation scalaire de convection
Keywords:
convection equation, transport equation, shock waves, finite element method, Lax-Wendroff scheme, fluctuation splittingAbstract
The principal goal of this papers is the development of numerical models to capture shock waves in compressible flows. In this first part we should only resolve the scalar convection equation. An explicit scheme for time discretization and FEM with linear triangular element for the space discretization should be employed. We have investigated two approaches. The first one, called the LWR method, is a centered sheme while the other one is the Fluctuation Splitting method based on an upwinding scheme. Initiallv, the second method was developed in a Finite Volume context, however we have rewriten it in a FE context by suitable choice of weighted functions. These methods are applied to different 2-D scalar convection equation examples.
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