Abstract
A comprehensive analysis of the one-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates is performed. One of the representations of these equations in Lagrangian coordinates is given by a single second-order partial differential equation. Symmetries of this equation are analyzed using the entropy for the group classification. Noether’s theorem is applied for constructing conservation laws. The obtained conservation laws are represented in the gas dynamics variables in Lagrangian coordinates and in Eulerian coordinates as well. Invariant and conservative difference schemes are discussed for the basic adiabatic case.
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