scholarly journals Conservation laws of the two-dimensional gas dynamics equations

2019 ◽  
Vol 112 ◽  
pp. 126-132 ◽  
Author(s):  
E.I. Kaptsov ◽  
S.V. Meleshko
Keyword(s):  
Conservation Laws ◽  
Gas Dynamics ◽  
Two Dimensional ◽  
Gas Dynamics Equations

scholarly journals METHOD OF ANALOGIES BETWEEN HYDRAULICS OF TWO-DIMENSIONAL WATER FLOWS AND GAS DYNAMICS

2020 ◽  
Vol 8 (2) ◽  
pp. 49-52 ◽  
Author(s):  
Maria Aleksandrova
Keyword(s):  
Gas Dynamics ◽  
Analytical Theory ◽  
Two Dimensional ◽  
Real Potential ◽  
Gas Dynamics Equations ◽  
Water Flows ◽  
Two Dimensional Flows

Real potential two-dimensional flows of practical hydraulics are considered, which can be considered with a certain accuracy as two-dimensional in terms, which confirms the relevance of the work. It is proposed to use the method of analogies when applying gas dynamics equations in hydraulics. An important result was obtained for the development of the analytical theory of two-dimensional potential water flows.

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.

Modeling the evolution of small distortions of the sphericity of a collapsing bubble

2007 ◽  
Vol 5 ◽  
pp. 60-65
Author(s):  
A.A. Aganin ◽  
Т.S. Guseva ◽  
Т.F. Khalitova
Keyword(s):  
Gas Dynamics ◽  
Spherical Shape ◽  
Heat Conducting ◽  
Full Model ◽  
Two Dimensional ◽  
Liquid Motion ◽  
Gas Dynamics Equations ◽  
Simplified Models ◽  
Spherical Component ◽  
Model Based

Results of calculating the evolution of small axisymmetric distortions of the spherical shape of a bubble during its collapse are presented. The full model based on two-dimensional gas dynamics equations (gas and liquid are considered inviscid non-heat-conducting) and a number of simplified models are used. The latter are obtained from the full model by splitting the gas and liquid motion into a spherical component and its small non-spherical perturbation. The differences of the simplified models are defined by the assumptions used in the realization of the splitting.

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