GA-hardness of dense-gas flow optimization problems

A study about convergence of Genetic Algorithms (GAs) applied to shape optimization problems for inviscid flows of real gases is presented. Specifically, working fluids of the Bethe - Zel'dovich - Thompson (BZT) type are considered, which exhibit non classical dynamic behaviors in the transonic/supersonic regime, such as the disintegration of compression shocks. A reference, single-objective optimization problem, namely, wave drag minimization for a non-lifting inviscid transonic flow past a symmetric airfoil is considered. Several optimizations runs are performed for perfect and BZT gases at different flow conditions using a GA. For each case, GA-hardness is measured, i.e. the capability of converging more or less easily toward the global optimum for a given problem. Numerical results show that GA-hardness increases for a class of problems, such that the flow field past the optimal airfoil is characterized by very weak shocks. In these conditions, reduced convergence rate and high sensitivity to the choice of the starting population are observed.