Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms

JOURNAL OF COMPUTATIONAL PHYSICS

卷:327

Article

Carrillo, Jose A.¹  Ranetbauer, Helene²  Wolfram, Marie-Therese^2,3 

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

[2] Austrian Acad Sci, Radon Inst Computat & Appl Math, Altenberger Str 69, A-4040 Linz, Austria

[3] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

关键词: Lagrangian coordinates;    Variational scheme;    Optimal transport;    Implicit in time discretization;   

DOI  :  10.1016/j.jcp.2016.09.040

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free