Numerical simulation of time-fractional partial differential equations arising in fluid flows via reproducing Kernel method

• Published in: International journal of numerical methods for heat & fluid flow Vol. 30; no. 11; pp. 4711 - 4733
• Main Author: Abu Arqub, Omar
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Publishing Limited 15.10.2020; Emerald Group Publishing Limited
• Subjects: Algorithms; Computational fluid dynamics; Differential equations; Fluid flow; Fractional calculus; Hilbert space; Infinite series; Kernels; Mathematical functions; Mathematical models; Multiphase flow; Partial differential equations; Physics; Simulation; Time-fractional partial differential equations; Reproducing kernel method; Robin functions types; Tricomi equation; Keldysh equation
• ISSN: 0961-5539; 1758-6585
• DOI: 10.1108/HFF-10-2017-0394

Purpose The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering. The purpose of this paper is to present results on the numerical simulation for time-fractional partial differential equations arising in transonic multiphase flows, which are described by the Tricomi and the Keldysh equations of Robin functions types. Design/methodology/approach Those resulting mathematical models are solved by using the reproducing kernel method, which provide appropriate solutions in term of infinite series formula. Convergence analysis, error estimations and error bounds under some hypotheses, which provide the theoretical basis of the proposed method are also discussed. Findings The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the prospects of the gained results and the method are discussed through academic validations. Originality/value In this paper and for the first time: the authors presented results on the numerical simulation for classes of time-fractional PDEs such as those found in the transonic multiphase flows. The authors applied the reproducing kernel method systematically for the numerical solutions of time-fractional Tricomi and Keldysh equations subject to Robin functions types.