A novel Bessel–Newton algorithm for the simulation of 2D laminar flow between two moving porous walls problem

This work investigates the two-dimensional laminar flow of fluid between two moving porous walls, a key problem in fluid mechanics with implications in filtration, chemical engineering, and biomedical devices. The difficulty resides in precisely and effectively solving the governing nonlinear differential equations that characterize such flows. We propose a unique Bessel–Newton algorithm that utilizes the Bessel operational matrices collocation method for discretizing the equations and employs a Newton iterative strategy to resolve the resulting nonlinear system. This integrated approach guarantees swift convergence and superior computing efficiency. The principal findings indicate that the suggested method attains enhanced accuracy, with errors diminished by multiple orders of magnitude relative to current numerical techniques, across various flow parameters including Reynolds number and wall dilation rate. The convergence study and error bounds confirm the method’s resilience. The study indicates that the Bessel–Newton algorithm is a robust and dependable tool for modeling fluid flow in porous media, surpassing existing methods in both accuracy and efficiency. This study is novel due to its application of Bessel functions to address intricate boundary conditions and its capacity to attain high accuracy with reduced computer resources, hence advancing numerical approaches in fluid mechanics.