Pressure-based Semi-analytical Solution of Radial Stokes Flows

A semi-analytical methodology is proposed and implemented to approximate the solution of the partial differential equations that model the radial Stokes flow between two parallel disks. Two traditional approaches for solving partial differential equations of mathematical physics, namely, eigenfunction expansions and Green’s function representations, are used to obtain directly the pressure distribution for a variety of inflow boundary conditions. We combine these standard techniques with a functional analytic framework to propose a proper representation for the pressure. This methodology has been implemented first in a symbolic software MathematicaW. and then numerically. We provide both validation of the methodology when an exact solution exists and comparison with a spectral element solver for a test case where inflow boundary conditions render the existence of a recirculation zone close to the entrance of the domain. We briefly discuss how to extend the methodology to handle the Navier]Stokes equation in radial flow}a subject that will be presented in detail in a following paper.