We are pleased to announce that Philippe Angot, professor at the Aix-Marseille University (France), will give the SFB 1313 "Pretty Porous Science Lecture" #59. His talk will be on "On the unsteady Navier-Stokes problem with a nonlinear open boundary condition modeling a singular load".
Date: Tuesday, 17 December 2024
Time: 4 pm CET
Speaker: Prof. Philippe Angot, Aix-Marseille Université (France)
Lecture title: "On the unsteady Navier-Stokes problem with a nonlinear open boundary condition modeling a singular load"
Place: 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 non linear 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.
About Philippe Angot
Dr. Philippe Angot is currently Professor of mathematics at Aix-Marseille University, working as a researcher at the ’Institut de Math´ematiques de Marseille’. He has published more than 50 articles in international Journals and more than 40 papers in refereed Proceedings. He has also supervised 15 Ph.D.’s theses. His research topics mainly concern applied analysis including analysis and numerical analysis of partial differential equations and scientific computing, as well as mathematical and numerical modeling of fluid flow or coupled fluid-porous flow problems. Since more recently, his research came also to some issues in real or Fourier analysis and analytical number theory.