ABSTRACT We consider the effects of granulation with a complex geometry of a magnetic carpet on the genesis of waves and plasma flows in a quiet-region of the solar atmosphere. Our aim is to perform numerical experiments on the self-generated and self-evolving solar granulation in a magnetic carpet representing the parts of the large-scale magnetized solar atmosphere, where waves and flows are basic inherent physical processes occurring continuously. We perform numerical experiments with the use of the joanna code which solves non-ideal and non-adiabatic two-fluid equations for ions + electrons and neutrals treated as two separate fluids. In these experiments, we assume that the plasma is hydrogen, and initially described by magnetohydrostatic equilibrium which is accompanied with a magnetic carpet. Parametric studies with different values of magnetic field show that its higher values result in larger magnitudes of ion-neutral velocity drift, thus ensuring larger heating and plasma flows. The present model addresses that in the highly dynamic solar chromosphere, waves, heating and plasma flows may collectively couple different layers of the solar atmosphere, and this entire process crucially depends on the local plasma and magnetic field properties. We suggest that waves and flows are the natural response of the granulation process in the quiet-Sun.