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arXiv · 1411.1012

A variational time discretization for the compressible Euler equations

Fabio Cavalletti·Marc Sedjro·Michael Westdickenberg
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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.

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Fabio Cavalletti, Marc Sedjro, Michael Westdickenberg. 2014-10-23. A variational time discretization for the compressible Euler equations. https://arxiv.org/abs/1411.1012

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