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Journal Articles SIAM Journal on Applied Mathematics Year : 2023

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

Abstract

We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the particular case of gradient flows, the schemes dissipate the free energy at the fully discrete level. Moreover, these schemes are generalised to coupled systems of non-linear continuity equations, such as multispecies models in mathematical physics or biology, preserving the bounds and the dissipation of the energy whenever applicable. These results are illustrated through extensive numerical simulations which explore known behaviours in biology and showcase new phenomena not yet described by the literature.

Dates and versions

hal-03541876 , version 1 (24-01-2022)

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Rafael Bailo, José Antonio Carrillo, Jingwei Hu. Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation. SIAM Journal on Applied Mathematics, 2023, 83 (3), pp.1315-1339. ⟨10.1137/22M1488703⟩. ⟨hal-03541876⟩
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