Title: Integrated intelligent Jaya Runge-Kutta method for solving Falkner-Skan equations with various wedge angles

Authors: Hongwei Guo; Xiaoying Zhuang; Timon Rabczuk

Addresses: Department of Geotechnical Engineering, Tongji University, Shanghai, China; Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, China; Computational Science and Simulation Technology, Institute of Photonics, Leibniz Universität Hannover, Hannover, Germany ' Department of Geotechnical Engineering, Tongji University, Shanghai, China; Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, China; Computational Science and Simulation Technology, Institute of Photonics, Leibniz Universität Hannover, Hannover, Germany ' ALISR Laboratory, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia

Abstract: In this work, the hybrid intelligent computing method is developed to solve the Falkner-Skan equations with various wedge angles, which combines efficient Jaya algorithm with classical Runge-Kutta method. Using higher order reduction strategies, the whole problem can be reduced to solving of coupled differential equations with prescribed initial and boundary conditions. The hybrid Jaya Runge-Kutta method is found to yield stable and accurate results and can extract those unknown parameters brought by asymptotic boundary condition in solving the coupled differential equations. In addition, the Jaya algorithm, without the need for tuning the algorithm-specific parameters, is proved to be effective and stable for optimisation problems. By comparing numerical results obtained using the Jaya algorithm with particle swarm optimisation (PSO), genetic algorithm (GA), hyperband, the hybrid Jaya Runge-Kutta method proves to be more stable and accurate, which shows great potential for solving more complicated multifield and multiphase flow problems.

Keywords: Jaya algorithm; Runge-Kutta method; hyperband; optimisation; PDEs; Falkner-Skan; boundary layer flow.

DOI: 10.1504/IJHM.2022.127047

International Journal of Hydromechatronics, 2022 Vol.5 No.4, pp.311 - 335

Received: 12 Feb 2022
Accepted: 05 May 2022
Published online: 18 Nov 2022 *

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