Structure of wall flow through a channel with a granular bed

Abstract

The problem of viscous incompressible fluid flow through a plane channel with one linear and one sinusoidal boundary is considered. Using the representation of the system of Stokes equations in terms of the stream function in a region including a single periodic element, we obtain a boundary-value problem for the biharmonic operator. Its solution is found by the mixed Galerkin method - the straight line method. The near-degenerate matrix of unknown coefficients was calculated on a computer. The velocity vector component, pressure and streamline fields are found as functions of the curvature of the boundary. The features of the flow structure resulting from the asymmetry of the walls are established. The distortion of the pore space required to refine the dependence of the permeability on the structure is introduced. The results are of interest for analyzing the wall effect of increased flow velocity in a channel with a fixed granular bed.