We introduce a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep requires the minimization of a functional measuring the acceleration of fluid elements, over the cone of monotone transport maps. We prove convergence to measure-valued solutions for the pressureless gas dynamics and the compressible Euler equations. For one space dimension, we obtain sticky particle solutions for the pressureless case.

A variational time discretization for compressible Euler equations / Cavalletti, Fabio; Sedjro, Marc; Westdickenberg, Michael. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 371:7(2019), pp. 5083-5155. [10.1090/tran/7747]

A variational time discretization for compressible Euler equations

Cavalletti, Fabio;
2019

Abstract

We introduce a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep requires the minimization of a functional measuring the acceleration of fluid elements, over the cone of monotone transport maps. We prove convergence to measure-valued solutions for the pressureless gas dynamics and the compressible Euler equations. For one space dimension, we obtain sticky particle solutions for the pressureless case.
371
7
5083
5155
https://arxiv.org/abs/1411.1012
Cavalletti, Fabio; Sedjro, Marc; Westdickenberg, Michael
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/95499
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