Group Analysis of One-Dimensional Gas Dynamics Equations in Lagrangian Coordinates and Conservation Laws

2020 ◽  
Keyword(s):  
Conservation Laws ◽  
Gas Dynamics ◽  
Group Analysis ◽  
Lagrangian Coordinates ◽  
Gas Dynamics Equations ◽  
One Dimensional

scholarly journals On invariant finite-difference schemes for equations of one-dimensional flows of a polytropic gas for problems with spatial symmetries

2021 ◽  
pp. 1-34
Author(s):  
Aleksander Alekseevich Russkov ◽  
Evgeny Igorevich Kaptsov
Keyword(s):  
Conservation Laws ◽  
Gas Dynamics ◽  
State Equation ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Local Conservation ◽  
Gas Dynamics Equations ◽  
One Dimensional ◽  
Polytropic Gas ◽  
Invariant Properties

One-dimensional polytropic gas dynamics equations for plane, radially symmetric, and spherically symmetric flows are considered. Invariant properties of equations are discussed, local conservation laws are derived. Additional conservation laws are written, which take place only in case of special values of adiabatic exponent. Classical difference scheme of Samarsky-Popov for gas dynamics has all difference analogs of conservation laws, except for additional ones. In difference schemes additional conservative laws take place in case of special state equation approximation. Scheme of Samarsky-Popov with special state equation was initially suggested by V.A. Korobitsyn. He described it as ‘thermodynamically consistend’ In current paper group properties, and conservation laws of thermodynamically consistent schemes are discussed, and numerical implementation for plane, cylinder, and spherical flows is perfomed.

ASYMPTOTICAL ANALYSIS OF ONE DIMENSIONAL GAS DYNAMICS EQUATIONS

2001 ◽  
Vol 6 (1) ◽  
pp. 117-128 ◽  
Author(s):  
A. Krylovas ◽  
R. Čiegis
Keyword(s):  
Gas Dynamics ◽  
Numerical Experiments ◽  
Method Of Averaging ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Resonance Case ◽  
Gas Dynamics Equations ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Asymptotical Analysis

A method of averaging is developed for constructing a uniformly valid asymptotic solution for weakly nonlinear one dimensional gas dynamics systems. Using this method we give the averaged system, which disintegrates into independent equations for the non‐resonance systems. Conditions of the resonance for periodic and almost periodic solutions are presented. In the resonance case the averaged system is solved numerically. Some results of numerical experiments are given.

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