Conservative difference schemes for one-dimensional flows of polytropic gas

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.

Cited by in corpus (4)

• Shallow water equations in Lagrangian coordinates: symmetries, conservation laws and its preservation in difference models
• Invariant conservative difference schemes for shallow water equations in Eulerian and Lagrangian coordinates
• Invariant finite-difference schemes with conservation laws preservation for one-dimensional MHD equations
• One-dimensional flows of a polytropic gas: Lie group classification, conservation laws, invariant and conservative difference schemes