Group theoretic approach and analytical solutions of the compressible Navier-Stokes equations

TL;DR

This paper applies group theoretic methods to analyze the compressible Navier-Stokes equations, deriving symmetry groups and self-similar solutions, including graphical illustrations, advancing analytical solution techniques.

Contribution

It computes the 12-dimensional Lie symmetry group and derives new self-similar solutions for the compressible Navier-Stokes equations.

Findings

Lie symmetry group of the equations is 12-dimensional

Self-similar solutions are explicitly constructed

Graphical illustrations of solutions are provided

Abstract

A group theoretic analysis of the compressible Navier-Stokes equations of an ideal gas are carried out. The 12-dimensional Lie symmetry group is computed. The commutation table and the Levi decomposition of its Lie algebra are presented. The equations are reduced and self-similar one-, two- and three-dimensional solutions are computed. Many of them are graphically illustrated.