A variational time discretization for the compressible Euler equations
Analysis of PDEs
2018-10-01 v4
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.
Cite
@article{arxiv.1411.1012,
title = {A variational time discretization for the compressible Euler equations},
author = {Fabio Cavalletti and Marc Sedjro and Michael Westdickenberg},
journal= {arXiv preprint arXiv:1411.1012},
year = {2018}
}