A variational time discretization for compressible Euler equations

Cavalletti, Fabio; Sedjro, Marc; Westdickenberg, Michael

doi:10.1090/tran/7747

A variational time discretization for compressible Euler equations
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by Fabio Cavalletti, Marc Sedjro and Michael Westdickenberg PDF

Trans. Amer. Math. Soc. 371 (2019), 5083-5155 Request permission

Abstract:

We introduce a variational time discretization for the multidimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each time step 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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