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arXiv · 1912.06423

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

Anissa Keurti·Thomas Rey
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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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Anissa Keurti, Thomas Rey. 2019-12-13. Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions. https://arxiv.org/abs/1912.06423

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