Evolution of Lagrangian Manifolds and Asymptotic Solutions to the Linearized Equations of Gas Dynamics

2019 ◽  
Vol 24 (1) ◽  
pp. 80-89 ◽  
Author(s):  
Anna I. Allilueva ◽  
Andrei I. Shafarevich
Keyword(s):  
Gas Dynamics ◽  
Asymptotic Solutions ◽  
Linearized Equations ◽  
Equations Of Gas Dynamics ◽  
Lagrangian Manifolds

Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

2018 ◽  
Vol 13 (3) ◽  
pp. 59-63 ◽  
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Gas Dynamics ◽  
Hydrodynamic Type ◽  
System Of Equations ◽  
Two Dimensional ◽  
Equations Of Gas Dynamics ◽  
Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

A Time Marching Method for Internal Flows Using Curvilinear Coordinates

1986 ◽  
Vol 10 (1) ◽  
pp. 8-15
Author(s):  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Gas Dynamics ◽  
Curvilinear Coordinates ◽  
System Stability ◽  
Internal Flows ◽  
Axisymmetric Nozzle ◽  
Equations Of Gas Dynamics ◽  
Curvilinear Grid ◽  
Momentum Fluxes ◽  
Time Marching ◽  
Marching Method

A time-marching method for flows with nozzle and blade-to-blade applications is presented. The approach developed consists of solving the basic conservation equations of gas dynamics in conservation form on a curvilinear grid. The assumption of quasi-streamlines is satisfied by generating a body-fitted coordinate system. Stability is maintained by upwind differencing of the mass and momentum fluxes and downwind differencing of the pressure. The method is then applied to the solution of a plane and axisymmetric nozzle and to VKI’s gas turbine blade and compared to previous computations and experiments.

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