Colloquium

Free boundary flows involve the motion of a fluid in a region of space which is not fixed but it evolves in time depending on the fluid flow itself. Because of the large amount of variables and nonlinearities involved in the problem, partitioned algorithms seem to be a natural choice for the numerical solution of free boundary flows. Partitioned algorithms are based on the idea of splitting the original problem in a sequence of simpler sub-problems which involve only a sub-set of the unknowns and the equations of the original full problem. Unfortunately, to date, partitioned schemes available in literature are unstable when applied to free boundary flows where the interfacial coupling is highly nonlinear. This is the case in blood flow simulations and in coating flows. In this talk, we will present some new ideas on the development of efficient numerical solvers for free boundary flows with strong interfacial effects. Our objective is to obtain numerical schemes which combine good stability properties with affordable memory requirement, low computational costs and minimal implementation time. To reach this goal, we use the operator splitting technique to discretize in time the full coupled problem. The choice for the time-discretization is driven by the mathematical features of the interfacial nonlinearities arising through the conditions of continuity of stresses and velocities at the deformable interfaces. Numerical results will be discussed.