期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 327, 期 -, 页码 186-202出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2016.09.040
关键词
Lagrangian coordinates; Variational scheme; Optimal transport; Implicit in time discretization
资金
- Royal Society via a Wolfson Research Merit Award
- Austrian Academy of Sciences OAW via the New Frontiers Group [NSP-001]
- King Abdullah University of Science and Technology
- Engineering and Physical Sciences Research Council [EP/K008404/1] Funding Source: researchfish
- EPSRC [EP/K008404/1] Funding Source: UKRI
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.
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