On the continuity of mean total normal stress in geometrical multiscale cardiovascular problems

In this work an iterative strategy to implicitly couple dimensionally-heterogeneous blood flow models accounting for the continuity of mean total normal stress at interface boundaries is developed. Conservation of mean total normal stress in the coupling of heterogeneous models is mandatory to satisfy energetic consistency between them. Nevertheless, existing methodologies are based on modifications of the Navier-Stokes variational formulation, which are undesired when dealing with fluid-structure interaction or black box codes. The proposed methodology makes possible to couple one-dimensional and three-dimensional fluid-structure interaction models, enforcing the continuity of mean total normal stress while just imposing flow rate data or even the classical Neumann boundary data to the models. This is accomplished by modifying an existing iterative algorithm, which is also able to account for the continuity of the vessel area, when required. Comparisons are performed to assess differences in the convergence properties of the algorithms when considering the continuity of mean normal stress and the continuity of mean total normal stress for a wide range of flow regimes. Finally, examples in the physiological regime are shown to evaluate the importance, or not, of considering the continuity of mean total normal stress in hemodynamics simulations.