Implicit finite-difference computations of unsteady transonic flows about airfoils, including the treatment of irregular shock-wave motions

Continuous Dynamic Simulation for Morphing Wing Aeroelasticity

“…result in LCO. This reminds one of the famous oscillatory flap solutions of Tijdeman [14,15] in transonic flow, where a steady strong shock will result in small (unsteady) shock excursion (type A) and weak shocks will result in large-amplitude (unsteady) shock excursions (types B and C − Morph Angle Effect The flutter/LCO speeds increases with increased Γ, in spite of M = 0.9 or 0.95. Increasing Γ will enhance the wing torsional stiffness, leading to the large flutter dynamic pressure (see Table 1).…”

Spectral Methods for the Small Disturbance Equation of Transonic Flows

“…In this work we are concerned essentially with treating the shock using spectral methods. One may modify the spectral scheme to be implicit in time, and compare the results to an implicit scheme using the Murman-Cole switch [3], or the Engquist-Osher one [16]. …”

“…. -3 -Since the Shuman filter may reduce the accuracy of the scheme, we removed the two filters mentioned above for a few iterations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10) It turns out that we got the location of the shock very accurately, regardless of the number of iterations for which we have removed the two filters applied until reaching a steady state. The location of the shock agrees with that prescribed by the E -0 scheme using a grid which is four times finer in the E -0 scheme.…”

Stable and Entropy Satisfying Approximations for Transonic Flow Calculations

“…During the last few years many numerical calculations using these equations have been presented (see [1], [2], [6], [8], [12] and the bibliographies in these papers).…”

“…In this way it has been possible to avoid most nonphysical shocks and to keep the shock front sharper than in the case of uniform schemes. Variants of the Cole-Murman difference scheme [12] have been the basis for many successful calculations (see [1], [6], [8]). However, in [6] it is pointed out that the Cole-Murman scheme does admit entropy violating shocks as solutions, and furthermore in [1] and [8] instabilities are reported even if the schemes should be stable according to linear stability analysis.…”