Simulations of blood flows in arteries require numerical solutions of fluid-structure interactions involving Navier-Stokes equations coupled with large displacement visco-elasticity for the vessels. Among the various simplifications which have been proposed, the surface pressure model leads to a hierarchy of simpler models including one which involves only the pressure. The model exhibits fundamental frequencies which can be computed and compared with the pulse. Yet unconditionally stable time discretizations can be constructed by combining implicit time schemes with Galerkin-characteristic discretization of the convection terms in the Navier-Stokes equations. Such problems with prescribed pressure on the walls will be shown to be efficient and accurate as an approximation of the full fluid structure interaction problem.
