The finite element method in the solution of unbounded potential flows

✍ Scribed by Wagdi G. Habashi

• Publisher: John Wiley and Sons
• Year: 1979
• Tongue: English
• Weight: 660 KB
• Volume: 14
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620140908

✦ Synopsis

A simple, yet effective, finite element approach to aerodynamic problems is presented. A better approximation of the geometry is obtained by the mapping of airfoils into near-circles. The mapping serves in homogenizing the gradients of the problem by magnifying regions of high gradients such as the leading and trailing edges while geometrically condensing the lower gradient regions on the main part of the airfoil. The mapping also permits the use of an effective automated mesh generation scheme that greatly reduces the amount of preparatory work involved in finite elements. To limit the size of the solution domain, an asymptotic analytical solution, with unknown coefficients, is assumed on a finite radius outer contour. The coefficients are obtained along with the finite ekernent nodal unknowns. An accrued advantage of this patching asymptotic procedure is its ability to obtain the lift as a solution variable without having to resort to the numerical integration of the pressure field over the body. Solutions to non-lifting and lifting bodies are obtained.