Blade shape optimization based on adjoint Euler equations with a point-implicit relaxation algorithm

Abstract

This paper presents a point-implicit relaxation algorithm to solve adjoint Euler equations simply and with a short-computing time on a shape optimization with a sensitivity analysis. The adjoint Euler equations are adjoint equations derived from Euler equations. And the sensitivity analysis reveals how the factors, which you focus on, change as the other factors change. In the sensitivity analysis, the relation between these factors is derived by solving the adjoint equations, and the process of solving the equations is treated as same as that of solving the governing equations related with the adjoint equations. On a shape optimization process, an implicit time integration method is better to introduce than an explicit time integration method to reduce the time until the convergence of the shape. And since we have to develop another numerical scheme to solve them, the algorism is desired to be simple. This paper shows how to develop the algorithm and how the algorithm performs.