Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms, to appear in J. Comp. Phys.
File(s)
Accepted version
Author(s)
Carrillo de la Plata, J
Ranetbauer, H
Wolfram, MT
Type
Journal Article
Abstract
In this paper we present a numerical scheme for nonlinear continuity equations, which is
based on the gradient ow 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 ow 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 properties with
various examples in spatial dimension one and two.
based on the gradient ow 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 ow 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 properties with
various examples in spatial dimension one and two.
Date Issued
2016-09-22
Date Acceptance
2016-09-17
Citation
Journal of Computational Physics, 2016, 327, pp.186-202
ISSN
1090-2716
Publisher
Elsevier
Start Page
186
End Page
202
Journal / Book Title
Journal of Computational Physics
Volume
327
Copyright Statement
© 2016 Elsevier Inc. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
The Royal Society
Grant Number
WM120001
Subjects
Applied Mathematics
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published