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...

Steady and unsteady experimental data are presented for several xed geometry conditions from a test in the NASA Langley 0.3-Meter Transonic Cryogenic Tunnel. The purpose of this test was to obtain unsteady data for transonic conditions on a xed and pitching supercritical airfoil at high Reynolds numbers. Data and brief analyses for several of the xed geometry test conditions will be presented h...

This article presents the latest developments of an algebraic multigrid (AMG) based on full potential equation (FPE) solver for transonic flow problems with emphasis on advanced applications. The mathematical difficulties of the problem are associated with the fact that the governing equation changes its type from elliptic (subsonic flow) to hyperbolic (supersonic flow). The flow solver is capa...

A computational method for accurately predicting the static aeroelastic deformations of typical transonic transport wind tunnel models is described. The method utilizes a finite element method (FEM) for predicting the deformations. Extensive calibratiodvalidation of this method was carried out using a novel wind-off wind tunnel model static loading experiment and wind-on optical wing twist meas...

High-performance airfoils for transonic flows of Bethe–Zel’dovich–Thompson fluids are constructed using a robust and efficient Euler flow solver coupled with a multi-objective genetic algorithm. Bethe–Zel’dovich– Thompson fluids are characterized by negative values of the fundamental derivative of gasdynamics for a range of temperatures and pressures in the vapor phase, which leads to nonclassi...

An algorithm for computing transonic flow fields about fighter-type aircraft is described in the paper. The compressible Euler equations are solved numerically using a vertex-based, finite volume multigrid scheme. The space around the aircraft is discretized with a single-block H-0 mesh which is generated by the union of separate Omeshes around successive cross sections of the aircraft. The dis...

We close by describing two rather unusual applications of complex variables. The details are beyond the scope of this book, but the ideas involved definitely deserve mention. The first area of application is fluid dynamics. It was observed already in the nineteenth century that the equations describing the incompressibility and irrotationality of fluids are just the Cauchy-Riemann equations for...