Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms

José A. Carrillo, Helene Ranetbauer, Marie-Therese Wolfram

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large class of nonlinear continuity equations, whose dynamics are driven by internal energies, given external potentials and/or interaction energies. The solver is based on its variational formulation as a gradient flow with respect to the Wasserstein distance. Positivity of solutions as well as energy decrease of the semi-discrete scheme are guaranteed by its construction. We illustrate this property with various examples in spatial dimension one and two.
Original languageEnglish (US)
Pages (from-to)186-202
Number of pages17
JournalJournal of Computational Physics
StatePublished - Sep 22 2016
Externally publishedYes


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