Existence of solutions and continuous and semi-discrete stability estimates for 3D/0D coupled systems modelling airflows and blood flows

In this paper we analyse geometric multiscale models arising in the description of physiological flows such as blood flow arteries or air bronchial tree. The geometrical complexity networks which air/blood lead to a classical decomposition two areas: truncated 3D geometry corresponding largest contribution domain, and 0D part connected part, modelling smaller airways/vessels. fluid is described by Stokes Navier–Stokes system coupled so-called Windkessel models. resulting Navier–Stokes–Windkessel involves Neumann non-local boundary conditions that depends on considered applications. We first show different types share similar formalism. Next derive existence results stability estimates for continuous Stokes–Windkessel problem well semi-discretized systems with either implicit explicit treatment conditions. all calculations, pay special attention dependency various constants smallness data respect physical numerical parameters. particular exhibit kinds behavior depending model. Moreover even if no energy can be derived norms system, leading possible observed instabilities large applied pressures, both semi-discrete problems, obtained appropriate small enough introducing new chosen Stokes-like operator. These sufficient may give hint order magnitude enabling stable computations without stabilization method problem. Numerical simulations illustrate some theoretical results.