Periodic viscous flow: A bench‐mark problem

Abstract

AbstractA double‐transform technique provides a semi‐analytic solution in the form of a series expansion for unsteady axisymmetric Stokes flow in the entrance region of a semi‐infinite rigid cylindrical tube. This in turn offers an appropriate bench‐mark problem for evaluating the quality of numerical approximations. To illustrate this, periodic axial flow in a circular cylinder is considered. Some aspects of the bench‐mark problem that are of interest include the reverse flow in the wall layers, the accuracy of the approximate method in different flow regimes and the mesh grading. This bench‐mark problem and the numerical study provide some insight into practical issues pertinent to the approximate solution of unsteady and periodic flows.