error analysis and consistent splitting method

Isi

Hi everybody!!

I am trying to solve Navier-Stokes equations with incompressible and laminar flow.

The scheme I have chosen is a consistent splitting method in order to decoupled velocity and pressure.

The temporal scheme is a semi-implicit one; Diffusion matrix is treated implicity and Convection matrix and pressure are treated explicity.

As space discretization I am using finite element method.

As a benchmark I use Kim and Moin problem. And I am calculating the error as the time step decreases in both variables, velocity and pressure.

I calculate the velocity error with Lmax(T=[0,1],L2(space)) and the pressure error with L2(T=[0,1],L2(space))

The weird thing is that I obtain the following errors as the time step value decreases:

incrT=0.03125; error_vel=0.00247964; error_pre=0.00176696

incrT=0.015625; error_vel=0.00262931; error_pre=0.00187242

incrT=0.0078125; error_vel=0.00290054; error_pre=0.00196216

In all cases, the solution I obtain is really similar to the exact solution, but, as you can see, the error is bigger as the time_step_value decreases, something absolutely wrong.

I have checked the code several times and I cannot see the problem, could you give me any advice? Thanks in advance. Isi