  We performed numerical simulations of blood flow in arteries with a variable
stiffness and cross-section at rest using a finite volume method coupled with a
hydrostatic reconstruction of the variables at the interface of each mesh cell.
The method was then validated on examples taken from the literature. Asymptotic
solutions were computed to highlight the effect of the viscous and viscoelastic
source terms. Finally, the blood flow was computed in an artery where the
cross-section at rest and the stiffness were varying. In each test case, the
hydrostatic reconstruction showed good results where other simpler schemes did
not, generating spurious oscillations andnonphysical velocities.
