# Conservative difference schemes for one-dimensional flows of polytropic gas

## TL;DR

This paper develops difference schemes for one-dimensional polytropic gas flows that preserve key conservation laws, including mass, energy, and momentum, especially for specific adiabatic exponents related to the spatial dimension.

## Contribution

It introduces difference schemes with enhanced conservation properties for polytropic gas flows at special adiabatic exponents, extending previous schemes.

## Key findings

- Schemes conserve mass and energy for all cases.
- Additional conservation laws are achieved at specific adiabatic exponents.
- Applicable to plain, radially symmetric, and spherically symmetric flows.

## Abstract

The paper considers one-dimensional flows of polytropic (calorically ideal) gas. These flows include three cases of gas dynamics: plain one-dimensional flows (one-dimensional space), radially symmetric flows in two-dimensional space and spherically symmetric flows in three-dimensional space. Starting with the difference schemes which have conservation laws of mass and energy (as well as conservation of momentum and the center of mass motion for the plain one-dimensional flows), we find difference schemes which also have additional conservation laws for the special values of the adiabatic exponent $\gamma = 1 + 1 /d $, where $d$ is the space dimension.