This paper presents a viscous compressible flow problem to which an equilibrium solution, in terms of density and velocity, can be given implicitly by elementary functions. The corresponding initial boundary value problem is solved by time discretization by the Crank-Nicolson method, Newton linearization and space discretization using multidomain Chebyshev collocation techniques. The physical interval is covered by subintervals of equal length. Each subinterval utilizes the same number of collocation points and each interface consists of one or two points. Six ways of patching are tested. All of them yield solutions with spectral accuracy for a few time steps, but only three are stable in the long run. Details of the density evolution are illustrated