The Lax–Friedrichs method in one-dimensional hemodynamics and its simplifying effect on boundary and coupling conditions

The discretization of reduced one-dimensional hyperbolic models of blood flow using the Lax–Friedrichs method is discussed. Deriving the well-established scheme from a relaxation approach leads to new simplified boundary and coupling conditions in vascular networks accounting e.g. for vascular occlusions and bifurcations. In particular, blood flow modeling in networks of vessels can be realized with minimal information on the eigenstructure of the coupled models. The scheme, a MUSCL-type extension and the coupling conditions are obtained evaluating a discrete relaxation limit. Numerical experiments in uncoupled and coupled cases verify the consistency and convergence of the approach.