Conference Papers Year : 2020

Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions

Abstract

We present a new finite volume method for computing numerical approximations of a system of nonlocal transport equation modeling interacting species. This method is based on the work [F. Delarue, F. Lagoutire, N. Vauchelet, Convergence analysis of upwind type schemes for the aggregation equation with pointy potential, Ann. Henri. Lebesgue 2019], where the nonlocal continuity equations are 10 treated as conservative transport equations with a nonlocal, nonlinear, rough velocity field. We analyze some properties of the method, and illustrate the results with numerical simulations.
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hal-02408246 , version 1 (13-12-2019)

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Anissa El Keurti, Thomas Rey. Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions. International Conference on Finite Volumes for Complex Applications, Jun 2020, Bergen, Norway. ⟨10.1007/978-3-030-43651-3_20⟩. ⟨hal-02408246⟩
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