Linking an Artery to the Circulation: Introducing a Quasi-Simultaneous Coupling Approach for Partitioned Systems in Hemodynamics

When modeling complex systems such as the cardiovascular circulation one often needs to separate the problem into smaller subproblems because of the heterogeneous nature of the system and/or the modeling techniques. The application at hand is to link blood flow in an artery to that in the circulation. The artery of interest is modeled by a 3D CFD model that includes a model for the elastic wall to simulate fluid-structure interaction. This 3D arterial model is coupled to a 0D model (electric network) for the cardiovascular circulation. We show that the weak coupling method is numerically unstable for this application. Using a simple model problem, a theoretical stability analysis is performed which explains the instability of the simulation results. Additionally, we consider fluid-structure interaction in an elastic artery. Again stability analysis results in a theoretical (in) stability condition that is in good agreement with simulation results. As a solution for these stability problems the quasi-simultaneous method is presented. The big advantage over strongly coupled methods is its low computational cost.