Work

A variational time discretization for compressible Euler equations

Year: 2018

Type: article

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.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/7747

Authors: Fabio Cavalletti, Marc Sedjro, Michael Westdickenberg

Institutions: Scuola Internazionale Superiore di Studi Avanzati, African Institute for Mathematical Sciences, RWTH Aachen University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W771375565

FWCI: 2.433

Cites: 68

Cited by: 15

Related to: 20