TAYLOR GALERKIN SOLUTION OF THE TIME DEPENDENT NAVIER STOKES EQUATIONS
This paper describes an accurate finite element method for the solution of transient problems in incompressible viscous flows. Such problems are encountered in various domains of engineering and physical sciences, ranging from nuclear reactor post- accident heat removal studies to geophysical fluid dynamics analysis. The general philosophy behind the proposed approach is that an algorithm is successful if its various elemental components are designed to deal each with a specific part of the equations. To this end, the governing equations are split in time by a fractional step method in order to isolate the different spatial operators. First, the time approximation of the dynamic effect of each operator is performed through a Taylor expansion to derive the most appropriate method to mimic the corresponding physical phenomena. As far as the incompressibility condition is concerned, a projection method based on an orthogonal decomposition theorem is used, as suggested by Chorin in a finite difference context. The spatial discretization is then carried out according to the standard Galerkin finite element method. The combination of the Taylor approach for the time discretization with the Galerkin method for the space approximation guarantees a proper matching of the two discretization processes, particularly in the treatment of the convective phenomena which are dominant in most practical problems.
Bibliographic Reference: INTERNATIONAL CONFERENCE ON COMPUTATIONAL METHODS IN FLOW ANALYSIS, OKAYAMA, JAPAN, SEPT. 5-8, 1988, AVAILABILITY: CEC-LUXEMBOURG, DG-XIII/A2, BP 1907, MENTIONING PAPER ORA 33928 E
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Record Number: 1989126092700 / Last updated on: 1989-05-01
Available languages: en