A Novel Meshfree Method for Nonlinear Equations in Flow through Porous Media and Electrohydrodynamic Flows

Abstract

In this study, an efficient meshfree numerical method is introduced for solving the nonlinear boundary value problems. The method of fundamental solutions (MFS) is one of the most popular among meshfree methods. While traditionally limited to linear and homogeneous problems, this study extends the applicability of the MFS to include nonhomogeneous and nonlinear equations. To achieve this, an extended MFS is combined with a fixed-point iteration scheme. This developed framework is benchmarked to address two different flow problems. The first involves fluid flow through porous media in a channel governed by the nonlinear Brinkman-Forchheimer equation. The second problem pertains to electrohydrodynamic (EHD) flow in a circular conduit. The obtained solutions are compared with the finite element method and the solutions available in the existing literature.

Keywords:

• Extended MFS
• fixed point iteration
• nonlinear equation
• porous media
• EHD flow

Acknowledgments

ASR gratefully acknowledges the financial support by “SRG” (SRG/2021/000790) and “MATRICS” (MTR/2021/000417) schemes funded by the Science & Engineering Research Board, India.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was supported by the Science and Engineering Research Board.