Modified Navier–Stokes equations for the outflow boundary conditions in hemodynamics

Abstract

We present a new approach for the outflow boundary conditions of Navier–Stokes equations in hemodynamics. We first describe some existing 3D–0D coupling methods and highlight benefits and disadvantages of each of them. We then introduce a new method that consists in adding a 3D artificial part where the Navier–Stokes equations are modified to obtain an equivalent energy balance to a standard coupling with a 3-element Windkessel model. We investigate theoretically the stability of the system and compare it to previously introduced methods. Finally we compare these coupling methods for numerical simulations of blood flow in three patient-specific models, which represent different flow regimes in the pulmonary and systemic circulations. The new method, especially in its hybrid form, is a possible alternative to existing methods. It can be in particular convenient in codes that do not allow users to implement non-standard boundary conditions.