Search for Stationary Poiseuille Flows for an Incompressible Polymer Fluid in Channels with Perforated Walls
A. M. Blokhin1,2, R. E. Semenko1,2
1Novosibirsk State University, Novosibirsk, 630090, Russia
2Sobolev Institute of Mathematics (SIM), Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: viscoelastic fluid, Poiseuille flow, stationary solutions
Abstract
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.
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