Abstract: in this work, we introduce the unsteady incompressible Navier-Stokes equations with a new boundary condition, generalizes the Dirichlet and the Neumann conditions. Then we derive an adequate variational formulation of time-dependent Navier- Stokes equations. We then prove the existence theorem and a uniqueness result. A Mixed finite-element discretization is used to generate the nonlinear system corresponding to the Navier-Stokes equations. The solution of the linearized system is carried out using the GMRES method. In order to evaluate the performance of the method, the numerical results are compared with others coming from commercial code like Adina system.

Jaouad EL-Mekkaoui, Ahmed Elkhalfi and Abdeslam Elakkad, “Resolution of Unsteady Navier-stokes Equations with the C a,b Boundary condition” International Journal of Advanced Computer Science and Applications(IJACSA), 4(3), 2013. http://dx.doi.org/10.14569/IJACSA.2013.040308

@article{EL-Mekkaoui2013,
title = {Resolution of Unsteady Navier-stokes Equations with the C a,b Boundary condition},
journal = {International Journal of Advanced Computer Science and Applications},
doi = {10.14569/IJACSA.2013.040308},
url = {http://dx.doi.org/10.14569/IJACSA.2013.040308},
year = {2013},
publisher = {The Science and Information Organization},
volume = {4},
number = {3},
author = {Jaouad EL-Mekkaoui and Ahmed Elkhalfi and Abdeslam Elakkad}
}