Coupling 3D and 1D fluid–structure‐interaction models for wave propagation in flexible vessels using a finite volume pressure‐correction scheme

In this paper, a method is presented for the coupling of three‐dimensional (3D) and one‐dimensional (1D) fluid–structure‐interaction models for wave propagation phenomena in flexible vessels. The method is based on the hyperbolic nature of the 1D problem. More specifically, the two Riemann invariants of the 1D problem are expressed in terms of average velocity and pressure and the value of the invariant that approaches the 3D domain provides a non‐linear constraint between the two variables that is used as a boundary condition for the 3D problem. It is assumed that the distribution of the Riemann invariant is uniform in the vessel cross section. The implementation of the boundary condition in the context of a pressure‐correction solution method in a finite volume mesh is described in detail. Computations of pressure pulse propagation within an elastic cylindrical vessel showed that the wave propagates smoothly from the 3D to the 1D domain.