Transonic nozzle flows and free boundary problems for the full Euler equations

Transonic shocks and free boundary problems for the full Euler equations in infinite nozzles

We establish the existence, stability, and asymptotic behavior of transonic flows with a transonic shock for the steady, full Euler equations in two-dimensional infinite nozzles of slowly varying cross-sections. Given a smooth incoming flow that is close to a uniform supersonic state at the entrance, we prove that there exists a transonic flow whose infinite downstream smooth subsonic region is...

Transonic Flows about Oscillating Airfoils Using the Euler Equations

T r a n s o n i c f l ow o v e r a h a r m o n i c a l l y o s c i l l a t i n g a i r f o i l is computed by s o l v i n g t h e two-dimens ional E u l e r e q u a t i o n s i n i n t e g r a l form u s i n g t h e f i n i t e volume scheme. The d i s s i p a t i o n t e rms a r e c o n s t r u c t e d a c c o r d i n g t o t h e o r y of t o t a l v a r i a t i o n d i m i n i s h i n g schem...

Subsonic Flows for the Full Euler Equations in Half Plane

We study the subsonic flows governed by full Euler equations in the half plane bounded below by a piecewise smooth curve asymptotically approaching x1-axis. Nonconstant conditions in the far field are prescribed to ensure the real Euler flows. The Euler system is reduced to a single elliptic equation for the stream function. The existence, uniqueness and asymptotic behaviors of the solutions fo...

Comparison of the Full - Potential and Euler Formulations for Computing Transonic Airfoil Flows

Multidimensional Transonic Shocks and Free Boundary Problems for Nonlinear Equations of Mixed Type

We are concerned with the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as the following second-order nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential φ : Ω ⊂ R → R: ...