One-dimensional flows of a polytropic gas: Lie group classification, conservation laws, invariant and conservative difference schemes
arXiv:2011.14397 · doi:10.1007/978-981-16-4683-6_2
Abstract
The paper considers one-dimensional flows of a polytropic gas in the Lagrangian coordinates in three cases: plain one-dimensional flows, radially symmetric flows and spherically symmetric flows. The one-dimensional flow of a polytropic gas is described by one second-order partial differential equation in the Lagrangian variables. Lie group classification of this PDE is performed. Its variational structure allows to construct conservation laws with the help of Noether's theorem. These conservation laws are also recalculated for the gas dynamics variables in the Lagrangian and Eulerian coordinates. Additionally, invariant and conservative difference schemes are provided.
References in corpus (8)
- Continuous Symmetries of Difference Equations
- Continuous symmetries of Lagrangians and exact solutions of discrete equations
- Symmetry-preserving discrete schemes for some heat transfer equations
- A heat transfer with a source: the complete set of invariant difference schemes
- Shallow water equations in Lagrangian coordinates: symmetries, conservation laws and its preservation in difference models
- One-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates: symmetry classification, conservation laws, difference schemes
- Conservation Laws of the Two-Dimensional Gas Dynamics Equations
- Conservative difference schemes for one-dimensional flows of polytropic gas