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The charging of dust clouds and finite-sized porous insulating objects in flowing plasmas is studied by numerical simulations. Objects of regular and irregular shapes and different opacities (porosities) are investigated for different electron-to-ion temperature ratios and flow velocities. It is demonstrated that the opacity of the cloud or the porosity of an object has little effect on the plasma dynamics in their vicinity. The plasma can charge the interior of the objects, which can lead to a nontrivial contribution to the electric dipole moment and internal electric fields. The analysis is carried out in two spatial dimensions with the particle-in-cell DiP2D code.