An efficient semi-implicit finite volume method for axially symmetric compressible flows in compliant tubes

• New efficient semi-implicit finite-volume method for axially symmetric compressible flows in compliant tubes.
• The mathematical model includes incompressible flows in rigid tubes as well as a simple model for cavitation.
• The proposed method is able to handle all Mach number flows.
• Quasi-exact solution of the Riemann problem in compliant tubes.
• Computation of radial velocity profiles and wall shear stress from first principles.

In the present paper a new efficient semi-implicit finite volume method for the simulation of weakly compressible, axially symmetric flows in compliant tubes is presented. The fluid is assumed to be barotropic and a simple cavitation model is also included in the equation of state in order to model phase transition when the fluid pressure drops below the vapor pressure. The discretized flow equations lead to a mildly nonlinear system of equations that is efficiently solved with a nested Newton technique. The new numerical method has to obey only a mild CFL condition based on the flow velocity and not on the sound speed, leading to large time steps that can be used. The scheme behaves well in the presence of shock waves and phase transition, as well as in the incompressible limit. In the present approach, the radial velocity profiles and therefore the wall friction coefficient are directly computed from first principles. In the compressible regime, the new method is carefully validated against quasi-exact solutions of the Riemann problem, while it is validated against the exact solution found by Womersley for an oscillatory flow in a rigid tube in the incompressible regime.