  We prove that some time Euler schemes for the 3D Navier-Stokes equations
modified by adding a Brinkman-Forchheimer term and a random perturbation
converge in $L^2(\Omega)$. This extends previous results concerning the strong
rate of convergence of some time discretization schemes for the 2D Navier
Stokes equations. Unlike the 2D case, our proposed 3D model with the
Brinkman-Forchheimer term allows for a strong rate of convergence of order
almost 1/2, that is independent of the viscosity parameter.
