Bio-inspired computational heuristics to study the boundary layer flow of the Falkner-Scan system with mass transfer and wall stretching

Abstract

In the present study, a bio-inspired computational intelligence technique is developed for finding the solutions of the celebrated Falkner-Skan equation arising in fluid mechanics problems using feed-forward Artificial Neural Networks (ANNs), Genetic Algorithms (GA), the Active-Set (AS) method and their combination namely a GA-AS approach. The differential equations based ANNs modeling of the Falkner-Skan system is constructed by defining an unsupervised error function. The training of the design parameters of ANNs is carried out with the help of viable global search through GAs and fine tuning of the results is achieved with an efficient local search using the AS method. The proposed scheme is applied to a number of scenarios for the Falkner-Skan system based on boundary layer flow over a moving wall with mass transfer in the presence of a free stream with power-law velocity distributions. The dynamics of the system are investigated for different cases of mass transfer and wall stretching. The proposed results are compared with analytical and numerical solutions to verify the correctness of the approach. The accuracy and convergence of the proposed solver are validated through sufficient large numbers of independent runs in terms of different performance indices based on mean absolute error, Thail’s inequality coefficient and Nash-Suitcliff efficiency. These solutions greatly enrich possible approaches for stochastic numerical solution of the celebrated Falkner-Skan system.