Random-Choice Based Hybrid Methods for One and Two Dimensional Gas Dynamics

1989 ◽  
pp. 630-639
Author(s):  
E. F. Toro
Keyword(s):  
Gas Dynamics ◽  
Hybrid Methods ◽  
Two Dimensional ◽  
Random Choice

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.

Steady small-disturbance transonic dense gas flow past two-dimensional compression/expansion ramps

2018 ◽  
Vol 848 ◽  
pp. 756-787 ◽  
Author(s):  
A. Kluwick ◽  
E. A. Cox
Keyword(s):  
Gas Dynamics ◽  
Gas Flow ◽  
External Forcing ◽  
Two Dimensional ◽  
Small Disturbance ◽  
Dense Gas ◽  
Dimensional Flow ◽  
Flow Past ◽  
Two Dimensional Flow ◽  
Dimensional Parameters

The behaviour of steady transonic dense gas flow is essentially governed by two non-dimensional parameters characterising the magnitude and sign of the fundamental derivative of gas dynamics ($\unicode[STIX]{x1D6E4}$) and its derivative with respect to the density at constant entropy ($\unicode[STIX]{x1D6EC}$) in the small-disturbance limit. The resulting response to external forcing is surprisingly rich and studied in detail for the canonical problem of two-dimensional flow past compression/expansion ramps.

Two-dimensional quasi-stationary flows in gas dynamics

1968 ◽  
Vol 64 (4) ◽  
pp. 1099-1108 ◽  
Author(s):  
A. G. Mackie
Keyword(s):  
Differential Equations ◽  
Unsteady Flow ◽  
Exact Solutions ◽  
Gas Dynamics ◽  
Two Dimensional ◽  
Independent Variables ◽  
Stationary Flows ◽  
First Case ◽  
Special Cases ◽  
Flow Round

In this paper we are concerned with the two-dimensional, unsteady flow of an inviscid, polytropic gas whose adiabatic index γ lies between 1 and 3. We recall that comparatively early in the study of gas dynamics we encounter two exact solutions of gas dynamic problems. One, in one-dimensional unsteady flow, is the expansion of a semi-infinite column of gas which is initially at rest behind a piston which, at time t = 0, begins to move with constant speed away from the gas. The second, in two-dimensional, steady, supersonic flow, is the Prandtl–Meyer flow round a sharp convex corner. Both of those flows may be regarded as special cases of more general exact solutions which are obtained by the method of characteristics (see, for example, Courant and Friedrichs(1)). On the other hand, each may be obtained directly from the appropriate equations by making use of the fact that, in so far as neither problem contains any characteristic length parameter in its formulation, the principle of dynamic similarity can be used to reduce the system of partial differential equations to one of ordinary differential equations. In the first case the independent variables x and t occur only in the combination x/t and in the second the independent variables x and y occur only in the combination x/y. Interesting and instructive as the derivation of these solutions from such principles may be, it is an unfortunate fact that they are the only non-trivial solutions of the respective equations. This is not altogether surprising as the equations are ordinary with (in this case) a limited number of non-trivially distinct solutions.

Gas dynamics of laser ablation: two-dimensional expansion of the vapor in an ambient atmosphere

2001 ◽  
Author(s):  
Andrey V. Gusarov ◽  
Alexey G. Gnedovets ◽  
Igor Smurov
Keyword(s):  
Laser Ablation ◽  
Gas Dynamics ◽  
Ambient Atmosphere ◽  
Two Dimensional

Lagrangian random choice method for steady two-dimensional supersonic/hypersonic flow

AIAA Journal ◽  
1993 ◽  
Vol 31 (12) ◽  
pp. 2193-2194 ◽  
Author(s):  
C. Y. Loh ◽  
W. H. Hui
Keyword(s):  
Hypersonic Flow ◽  
Two Dimensional ◽  
Random Choice ◽  
Random Choice Method ◽  
Choice Method
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