scholarly journals One-Dimensional Flows of a Polytropic Gas: Lie Group Classification, Conservation Laws, Invariant and Conservative Difference Schemes

2021 ◽  
pp. 61-98
Author(s):  
V. A. Dorodnitsyn ◽  
R. Kozlov ◽  
S. V. Meleshko
Keyword(s):  
Conservation Laws ◽  
Lie Group ◽  
Group Classification ◽  
Difference Schemes ◽  
One Dimensional ◽  
Polytropic Gas ◽  
Conservative Difference Schemes ◽  
Lie Group Classification ◽  
Conservative Difference

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.

Lie group classification of the N-th-order nonlinear evolution equations

2011 ◽  
Vol 54 (12) ◽  
pp. 2553-2572 ◽  
Author(s):  
ShouFeng Shen ◽  
ChangZheng Qu ◽  
Qing Huang ◽  
YongYang Jin
Keyword(s):  
Lie Group ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Group Classification ◽  
Nonlinear Evolution Equations ◽  
Lie Group Classification

Lie group classification of second-order ordinary difference equations

2000 ◽  
Vol 41 (1) ◽  
pp. 480-504 ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Roman Kozlov ◽  
Pavel Winternitz
Keyword(s):  
Lie Group ◽  
Difference Equations ◽  
Group Classification ◽  
Second Order ◽  
Lie Group Classification
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