# One-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates: symmetry classification, conservation laws, difference schemes

## TL;DR

This paper performs a symmetry classification and conservation law analysis of one-dimensional polytropic gas dynamics equations in Lagrangian coordinates, and discusses invariant difference schemes for the adiabatic case.

## Contribution

It provides a complete Lie group classification of these equations and constructs conservation laws using Noether's theorem, including difference schemes for the adiabatic case.

## Key findings

- Complete symmetry classification based on entropy parameter
- Construction of conservation laws in gas dynamics variables
- Discussion of invariant difference schemes for the adiabatic case

## Abstract

Lie point symmetries of the one-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates are considered. Complete Lie group classification of these equations reduced to a scalar second-order PDE is performed. The classification parameter is the entropy. Noether theorem is applied for constructing conservation laws. The conservation laws can be represented in the gas dynamics variables. For the basic adiabatic case invariant and conservative difference schemes are discussed.