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23-05-2017

A Lagrangian Scheme à la Brenier for the Incompressible Euler Equations

Authors: Thomas O. Gallouët, Quentin Mérigot

Published in: Foundations of Computational Mathematics | Issue 4/2018

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Abstract

We approximate the regular solutions of the incompressible Euler equations by the solution of ODEs on finite-dimensional spaces. Our approach combines Arnold’s interpretation of the solution of the Euler equations for incompressible and inviscid fluids as geodesics in the space of measure-preserving diffeomorphisms, and an extrinsic approximation of the equations of geodesics due to Brenier. Using recently developed semi-discrete optimal transport solvers, this approach yields a numerical scheme which is able to handle problems of realistic size in 2D. Our purpose in this article is to establish the convergence of this scheme towards regular solutions of the incompressible Euler equations, and to provide numerical experiments on a few simple test cases in 2D.

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Metadata
Title
A Lagrangian Scheme à la Brenier for the Incompressible Euler Equations
Authors
Thomas O. Gallouët
Quentin Mérigot
Publication date
23-05-2017
Publisher
Springer US
Published in
Foundations of Computational Mathematics / Issue 4/2018
Print ISSN: 1615-3375
Electronic ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-017-9355-y

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