scholarly journals Conservation laws of the one-dimensional isentropic gas dynamics equations in Lagrangian coordinates

2019 ◽  
Author(s):  
Evgeniy I. Kaptsov ◽  
Sergey V. Meleshko
Keyword(s):  
Conservation Laws ◽  
Gas Dynamics ◽  
Lagrangian Coordinates ◽  
Gas Dynamics Equations ◽  
One Dimensional ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas ◽  
The One

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.

scholarly journals Stability and convergence of the difference schemes for equations of isentropic gas dynamics in Lagrangian coordinates

2012 ◽  
Vol 91 (105) ◽  
pp. 137-153
Author(s):  
Piotr Matus ◽  
Dmitry Polyakov
Keyword(s):  
Gas Dynamics ◽  
A Priori Estimates ◽  
Initial Boundary ◽  
Stability And Convergence ◽  
Lagrangian Coordinates ◽  
Smooth Functions ◽  
Differential Problem ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas ◽  
The Difference

For the initial-boundary value problem (IBVP) if isentropic gas dynamics written in Lagrangian coordinates written in terms of Riemann invariants we show how to obtain necessary conditions for existence of global smooth solution using the Lax technique. Under these conditions we formulate the existence theorem in the class of piecewise-smooth functions. A priori estimates with respect to the input data for the difference scheme approximating this problem are obtained. The estimates of stability are proved using only restrictions on the initial and boundary conditions corresponding the differential problem. In the general case the estimates have been obtained only for the finite instant of time t < t0. The monotonicity has been proved in the both cases. The uniqueness and convergence of the difference solution are also considered. The results of the numerical experiment illustrating theoretical statements are given.

Sign in / Sign up

Export Citation Format

Share Document