Try to solve N-S with some mesh method (finite difference, elements or volumes);

If you've already solved the initial boundary value problem just check the data files.

If visualization is the problem, you may try some free software (GNUplot or ParaView, for example)

Hi Anindya,

Do you mean to say that in your program the velocities are defined at the boundaries of your rectangular mesh element? and that you want to find it out at the center of the mesh element?

If that is so then I suggest a spatial interpolation would help.

You can download some of my earlier works  from this ResGate, where we've solved  similar CFD in natural coordinates by the FDM.

I believe you can interpolate the velocity on the boundaries of the zones to the center of the zone. This is how we do it, but there are various other ways.

Try to solve N-S with some mesh method (finite difference, elements or volumes);

If you've already solved the initial boundary value problem just check the data files.

If visualization is the problem, you may try some free software (GNUplot or ParaView, for example)

Dear Anindya,

You seem to be asking whether it is possible to find the velocity field at time t, at grid points at the interior of the rectangular domain, given that it is known at the boundaries. As has been remarked above by Alexander, you need to solve an initial value problem so you need to specify an initial incompressible velocity field throughout the mesh, that is consistent with the boundary conditions you want to impose at the rectangular boundary. Then you have to solve the Navier-Stokes equations numerically for the velocity field at the grid points using some mesh method such as finite difference. Ensuring incompressibility at each time step is one of the difficulties. There is plenty of literature about how this is done. Check any book on CFD.

On the rigid boundaries sharing sea from land, components of current velocity,  normal to the boundary surface are equal to zero; on the liquid boundaries connecting the sea with the  Strait and the River, values of velocityis given on the basis of experimental data.