Spectral Methods for the Small Disturbance Equation of Transonic Flows

Rarefaction wave interaction for the unsteady transonic small disturbance equations

We study a Riemann problem for the unsteady transonic small disturbance equations that results in a diverging rarefaction problem. The self-similar reduction leads to a boundary value problem with equations that change type (hyperbolic-elliptic) and a sonic line that is a free boundary. We summarize the principal ideas and present the main features of the problem. The flow in the hyperbolic par...

An Elliptic Problem Arising from the Unsteady Transonic Small Disturbance Equation

We prove a theorem on existence of a weak solution of the Dirich-let problem for a quasilinear elliptic equation with a degeneracy on one part of the boundary. The degeneracy is of a type (\Keldysh type") associated with singular behavior | blow-up of a derivative | at the boundary. We deene an associated operator which is continuous , pseudo-monotone and coercive and show that a weak solution ...

Weak Shock Reflection Modeled by the Unsteady Transonic Small Disturbance Equation

Adaptation of Structured Grid for Supersonic and Transonic Flows

Two distinct redistribution grids - adaptation techniques, spring analogy and elliptic grid generator are applied to two-dimensional steady, inviscid, shocked flows, and the ability of each technique is examined and compared. Euler equations are solved base on Roe's Reimann solver approach to simulate supersonic flow around a sphere, transonic flow about an airfoil and supersonic flow in a symm...

Fourier time spectral method for subsonic and transonic flows

The time accuracy of the exponentially accurate Fourier time spectral method (TSM) is examined and compared with a conventional 2nd-order backward difference formula (BDF) method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for ...