[en] We present a finite difference method for the numerical simulation of the axisymmetric countercurrent flow in a gas centrifuge. A time-marching technique is used to relax an arbitrary initial condition to the desired steady-state solution. All boundary layers can be resolved, and nonlinear effects may be included. Numerical examples are presented. We conclude that this technique is capable of predicting accurately the performance of a wide variety of machines under all operating conditions of interest