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13.5  PASS: Creeping Couette flow between cylinders

Stéphane Popinet
sh annulus.gfs
Required files
annulus.gfs (view) (download) error.ref
Running time
5 seconds

A polar coordinate system is used to solve the flow between two concentric cylinders. The inner cylinder is rotating and the outer cylinder is fixed. The tangential velocity profile is illustrated in Figure 177, together with the profile of a diffusive tracer with matching boundary conditions. The tracer profile involves a logr dependency whereas the velocity profile is polynomial in r. The difference is due to the metric terms appearing when diffusing vector quantities.

Figure 178 illustrates the convergence toward the analytical solution with spatial resolution.

Figure 177: Tangential velocity and tracer concentration as functions of radial position

Figure 178: Convergence of the error norms with spatial resolution.

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