Reconstruction of the velocities and pressures for a viscous fluid in a hollow cylinder

Abstract

We find the continuous velocities and pressures at all points of an incompressible viscous fluid flowing in a hollow cylinder from the given velocities at the points of some closed curves on the inner sides of the cylinder and the given pressures at two points on the inner sides of the cylinder. This solution can be named the interpolation solution. The solution is reduced to a succession of plane boundary problems for the elliptic differential equations. The method of solution is programmable and applicable for problems of piping, for example, for modelling a blood flow in a vessel with a fibrin on its inner surface. This method is illustrated by application to flow in a hollow circular cylinder with a rotation on the central level. The interpolation solution is the basis for the method of restoration of continuous velocities and pressures in the flow of an incompressible viscous fluid from the given velocities at a finite number of points on the inner surface of the cylinder and given pressures at two points on the same surface. © 2007 Elsevier Ltd. All rights reserved