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

2019/12/13 by Anissa El Keurti, Keurti, Anissa, Thomas Rey +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Geometric Analysis and Curvature Flows #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.1912.06423

openalex publication_date 2019/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new finite volume method for computing numerical approximations\nof a system of nonlocal transport equation modeling interacting species. This\nmethod is based on the work [F. Delarue, F. Lagoutire, N. Vauchelet,\nConvergence analysis of upwind type schemes for the aggregation equation with\npointy potential, Ann. Henri. Lebesgue 2019], where the nonlocal continuity\nequations are 10 treated as conservative transport equations with a nonlocal,\nnonlinear, rough velocity field. We analyze some properties of the method, and\nillustrate the results with numerical simulations.\n

Citations

• Convergence order of upwind type schemes for transport equations with\n discontinuous coefficients

Cited by

• Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation

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