The head of FLUPOR project, Prof. Dr. Philippe Angot, will present his works at the Institute of Applied Analysis and Numerical Simulation (IANS), University of Stuttgart.
- Talk: "On the unsteady Navier--Stokes problem with a nonlinear open boundary
condition modeling a singular load" - Time and place: December 17, 2024, at Multi Media Lab (MML), U1.003, Pfaffenwaldring 61, 70569 Stuttgart, Campus Vaihingen
- Abstract:
We present a practical nonlinear open boundary condition of Robin type for unsteady incompressible viscous flows taking account of the local inflow/outflow volume rate at an artificial open boundary with a singular load. The inflow/outflow parameters introduced in the modelling can be connected to the coefficient of singular head loss through Bernouilli's theorem of energy balance in a curl-free viscous flow.
Then, we prove that this boundary condition leads to a globally well-posed unsteady Navier--Stokes problem, {\em i.e.} global existence in time of a weak solution in dimension $d\leq 3$ with no restriction on the size of any data. The proof is carried out by passing to the limit on a sequence of consistent discrete solutions of a nonlinear numerical scheme which approximates the original problem. The main ingredients are Schauder's fixed-point theorem and Aubin-Lions compactness argument.
Moreover, numerical experiments show the efficiency and superiority of this nonlinear open boundary condition compared to the standard 'do nothing' condition.