Periodic viscous flow: A bench‐mark problem

Abstract

SUMMARYA 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.