Hydrosoft Journal
Dec. 1990
A Variational approach to
Navier-Stokes equations.
Khondaker, A.N.
,
Mohsen, M.F.N.,
Al-Layla, R.I.
Civil
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Abstract
A finite
element formulation is presented using an appropriate variational
form preserving the non-linearity of the Navier-Stokes equations. This variational function, previously used by Guymon and Scott,
in connection with the diffusion convection equation, is also found to be
viable for these non-linear equations. A solution algorithm was developed using
the 'vorticity' and 'stream function' formulation of
the Navier-Stokes equations. The dependent variables were approximated over
each triangular element using linear interpolation polynomials. The application
of the developed code to some numerical examples produced results comparable to
existing methods and displayed the efficiency of the method. The method was
found to be limited to low Reynolds numbers.