Search for stationary Poiseuille flows for an incompressible polymer fluid in channels with perforated walls

The problem of the flow of a viscoelastic fluid in a flat channel with permeable walls and a constant flow through the walls is considered. The problem is formulated using the equations of the modified Vinogradov–Pokrovskii mesoscopic model. For the case of the presence of a flow through the walls, a method for setting the boundary conditions is proposed, which ensures that the resulting solution is consistent with the solutions obtained with no account for the flow. A computational algorithm for finding solutions is considered both in the presence of flow through the walls and in its absence.