Modeling Refugee Movement Based on a Continuum Mechanics Phase-Field Approach of Porous Media
Lynn Schreyer Bennethum, Nikos Voulgarakis, Zachary T. Hilliard, Sergey Lapin, Loren Cobb · SIAM Journal on Applied Mathematics · 2021
Recent developments in the continuum mechanics methods for flow through porous media offer some unexpected benefits for modeling the flow of refugees during complex humanitarian emergencies as they move between locations. We develop a single, deterministic partial differential equation, in terms of number of people per area, that is a generalization of the Cahn--Hilliard equation in a manner that allows for future generalizations. The equation is numerically solved and demonstrates a plausible mass refugee movement under the influence of a perceived threat and nonuniform terrain conditions while moving in a group.