Venerdì 27 Marzo 2026, alle ore 16 in Aula U2-04 (Edificio U2 | Piazza della Scienza 3, Milano), Anika Beckers (RWTH Aachen University) terrà il seguente intervento
Titolo: Numerical Schemes for Multidimensional Nonlocal Conservation Laws
Abstract: In this talk, we present numerical schemes for two-dimensional systems of conservation laws with a flux that is nonlocal in space, i.e. the solution evolves over time depending on the nonlocal terms, which contain convolutions of the state variables with a mollifier. The underlying flux function is rather general to guarantee that our results are applicable to many models, such as crowd movements, material flow on conveyor belts or cluster formation. Nevertheless, we will focus on a model for crowd movements, regarding the pedestrians as density. The interaction between pedestrians in the form of mutual repulsion is included in the model and causes the nonlocal dependence of the flux. For the numerical approximation, we consider first-order schemes that are based on adapting well-known monotone numerical flux functions after approximating the nonlocal terms. We state sufficient conditions to ensure the convergence of these monotone-based numerical schemes to the unique weak entropy solution. Having established first-order accurate consistent numerical fluxes we use a CWENO reconstruction in space to derive higher-order numerical schemes. Applying a scaling limiter on the reconstruction ensures compliance with the maximum principle, including positivity preservation. However, the increased computational effort gives rise to challenges that must be addressed rigorously.
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