分野別セミナー

In this talk, we address two distinct but related topics:
First, we study the evolution of a gas-liquid mixture via a coupled system of elliptic-parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an unsaturated heterogeneous medium with distributed microstructures. Besides ensuring the well-posedness of our two-scale model, we design two-scale convergent numerical approximations and prove a priori error estimates and propose an a posteriori error estimator, used to propose a macroscopic mesh refinement strategy to achieve an overall error reduction. This is a joint work with Martin Lind and Adrian Muntean (Karlstad University, Sweden) Second, we study the evacuation dynamics of a crowd wanting to escape from a complex geometry in the presence of a fire as well as of a slowly spreading smoke curtain. The crowd we have in view is composed of two populations of individuals: one knowing the map of the building and one unaware of the given geometry, relying exclusively on potentially informed neighbors to identify a path of motion towards the exit. We demonstrate the hybrid crowd dynamics model with simulations and evacuation metrics. This is a joint work with Andrei Jalba (Eindhoven University of Technology, The Netherlands) and Adrian Muntean (Karlstad University, Sweden).

References:
1. O. M. Richardson, A. Jalba, and A. Muntean: Effects of environment knowledge in evacuation scenarios involving fire and smoke — a multiscale modelling and simulation approach, Fire Technology, 2018.
2. M. Lind, A. Muntean, and O. M. Richardson: Well-posedness and inverse Robin estimates for a multiscale elliptic/parabolic system, Applicable Analysis, 2018.
3. O. M. Richardson: Mathematical analysis and approximation of a multiscale elliptic-parabolic system, Licentiate thesis Karlstad university (to appear, 2018).