  We use a method based on the lubrication approximation in conjunction with a
residual-based mass-continuity iterative solution scheme to compute the flow
rate and pressure field in distensible converging-diverging tubes for
Navier-Stokes fluids. We employ an analytical formula derived from a
one-dimensional version of the Navier-Stokes equations to describe the
underlying flow model that provides the residual function. This formula
correlates the flow rate to the boundary pressures in straight cylindrical
elastic tubes with constant-radius. We validate our findings by the convergence
toward a final solution with fine discretization as well as by comparison to
the Poiseuille-type flow in its convergence toward analytic solutions found
earlier in rigid converging-diverging tubes. We also tested the method on
limiting special cases of cylindrical elastic tubes with constant-radius where
the numerical solutions converged to the expected analytical solutions. The
distensible model has also been endorsed by its convergence toward the rigid
Poiseuille-type model with increasing the tube wall stiffness.
Lubrication-based one-dimensional finite element method was also used for
verification. In this investigation five converging-diverging geometries are
used for demonstration, validation and as prototypes for modeling
converging-diverging geometries in general.
