One-dimensional flows of a polytropic gas: Lie group classification, conservation laws, invariant and conservative difference schemes
Mathematical Physics
2022-04-13 v1 Numerical Analysis
math.MP
Numerical Analysis
Abstract
The paper considers one-dimensional flows of a polytropic gas in the Lagrangian coordinates in three cases: plain one-dimensional flows, radially symmetric flows and spherically symmetric flows. The one-dimensional flow of a polytropic gas is described by one second-order partial differential equation in the Lagrangian variables. Lie group classification of this PDE is performed. Its variational structure allows to construct conservation laws with the help of Noether's theorem. These conservation laws are also recalculated for the gas dynamics variables in the Lagrangian and Eulerian coordinates. Additionally, invariant and conservative difference schemes are provided.
Keywords
Cite
@article{arxiv.2011.14397,
title = {One-dimensional flows of a polytropic gas: Lie group classification, conservation laws, invariant and conservative difference schemes},
author = {Vladimir A. Dorodnitsyn and Roman Kozlov and Sergey V. Meleshko},
journal= {arXiv preprint arXiv:2011.14397},
year = {2022}
}