Hydrosoft Journal

Dec. 1990

A Variational approach to Navier-Stokes equations.

Khondaker, A.N.Show author details, Mohsen, M.F.N.Show author details, Al-Layla, R.I.Show author details

Civil Engineering University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia



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.