Applications of the method of finite elements to fluid dynamics
The report presents some recent results relating to the application of the method of finite elements to the problems of fluid structure interaction. It begins with a description of motion in an arbitrary Lagrangian Eulerian (ALE) system. This generalised description of motion offers an optimal combination of the separate advantages of pure Lagrangian and pure Eulerian descriptions and is seen to be particularly useful for the treatment of the hydrodynamic domain. The conservation equations are presented in the differential form using the ALE description and hence the weak variable form is deduced, which allows the development of the integral models of these equations with respect to spatial variables using the Galerkin finite element method. Two variants of the method are outlined which stabilise the non-symmetrical convection operators. The report continues with a presentation of methods of integration with respect to time of the semi-integral conservation equations, resulting from the application of the method of finite elements. The cases of compressible fluids, where the effects of viscosity can be neglected, and of viscous incompressible fluids, are treated separately.
Bibliographic Reference: Article: Actes de l'Ecole d'Eté d'Analyse Numérique, Vol. 70 (1988), pp. 1-55
Record Number: 198910550 / Last updated on: 1994-12-01
Original language: fr
Available languages: en