Detailed study of complex flow fields of aerodynamical configurations by using numerical methods

Abstract

The mathematical physics of fluid flow in a compressible medium, leads to nonlinear partial differential equations or their equivalent integral versions. For the solution of these equations one has generally to resort to numerical methods using mostly finite difference or finite volume schemes, which are well established now. These field methods are very suitable for studying the physical features of complex flows. The present paper gives at first a short sketch of the numerical procedure and thereafter goes into the detailed analysis of the flow fields of delta wings, double-delta wings, delta shaped wing-canard combinations and space vehicles. Further examples include long span wings and wing-bodies at supercritical on flows, flows around propellers and rotors and finally some unsteady flows. The examples cited are selected topics from the extensive studies undertaken in the department of numerical aerodynamics of the DLR in Braunschweig in the course of the last few years.

An approximate analytical solution of the fractional multi-dimensional Burgers equation by the homotopy perturbation method

“…It is well known that the Navier-Stokes equations describe the physics of many phenomena of scientific and engineering interest. They may be used to model the weather prediction [22], fluid flow in a pipe [11], air flow around a wing of aircraft [9], discharge of the granular silo [28] and [33], etc. The Burgers equation has appeared frequently in various areas of applied mathematics fields such as acoustic transmission, shockwave, and gas dynamics (refer to [6,8], and [18]).…”