The phenomenon of Brinkman screening, whereby the fluid velocity disturbance produced by each particle in a fixed bed is attenuated by the forces that the fluid exerts on surrounding particles, plays a crucial role in limiting the range of velocity correlations in porous media and fixed beds. Koch and Brady [J. Fluid Mech. 154, 399 (1985)] showed theoretically that Brinkman screening leads to a finite hydrodynamic diffusion coefficient for fluid phase tracers in dilute fixed beds. In this Letter, we present the results of two simulation techniques (lattice-Boltzmann method and a multipole method) confirming the screening of the fluid velocity covariance that underlies the Koch and Brady theory.