Block-structured solution of Euler equations for transonic flows

AIAA Journal ◽  
1987 ◽  
Vol 25 (12) ◽  
pp. 1570-1576 ◽  
Author(s):  
Akin Ecer ◽  
John T. Spyropoulos ◽  
Vladimir Rubek
Keyword(s):  
Euler Equations ◽  
Transonic Flows ◽  
Block Structured

scholarly journals Analytic adjoint solutions for the quasi-one-dimensional Euler equations

2001 ◽  
Vol 426 ◽  
pp. 327-345 ◽  
Author(s):  
MICHAEL B. GILES ◽  
NILES A. PIERCE
Keyword(s):  
Boundary Condition ◽  
Euler Equations ◽  
Arbitrary Shape ◽  
Logarithmic Singularity ◽  
Adjoint Problem ◽  
Function Approach ◽  
Transonic Flows ◽  
One Dimensional ◽  
Adjoint Variables ◽  
Adjoint Solutions

The analytic properties of adjoint solutions are examined for the quasi-one-dimensional Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are continuous with zero gradient at the shock, and that an internal adjoint boundary condition is required at the shock. A Green's function approach is used to derive the analytic adjoint solutions corresponding to supersonic, subsonic, isentropic and shocked transonic flows in a converging–diverging duct of arbitrary shape. This analysis reveals a logarithmic singularity at the sonic throat and confirms the expected properties at the shock.

scholarly journals Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations

2018 ◽  
Vol 19 (4) ◽  
pp. 591-626
Author(s):  
Gui-Qiang Chen ◽  
Jun Chen ◽  
Mikhail Feldman
Keyword(s):  
Asymptotic Behavior ◽  
Euler Equations ◽  
Transonic Flows
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