Euler solutions for aerodynamic inverse shape design

Abstract

SUMMARYContributions to the aerodynamics development have to be involved to achieve an increase in quality, reducing time and computer costs. Therefore, this work develops an optimization method based on the ÿnite volume explicit Runge-Kutta multi-stage scheme with central spatial discretization in combination with multigrid and preconditioning. The multigrid approach includes local time-stepping and residual smoothing. Such a method allows getting the goal of compressible and almost incompressible solution of uid ows, having a rate of convergence almost independent from the Mach number. Numerical tests are carried out for the NACA 0012 and 0009 airfoils and three-dimensional wings based on NACA proÿles for Mach-numbers ranging from 0.8 to 0.002 using the Euler equations. These calculations are found to compare favorably with experimental and numerical data available in the literature. Besides, it is worth pointing out that these results build on earlier ones when ÿnding appropriate new three-dimensional aerodynamical geometries.

Inverse geometric design for a class of rotary positive displacement machines

“…To develop the inverse design models, Euler equations have been employed by researchers either in an inverse formulation, as employed by [10], or direct representation as used by [3] who use a multigrid approach that includes local time stepping accompanied by residual smoothing to find the inverse design solution. Of particular importance is the work of [4].…”