A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

Abstract

We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM), is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

An unsteady MHD Maxwell nanofluid flow with convective boundary conditions using spectral local linearization method

“…The transport equations have been solved using the iterative spectral local linearization method (SLLM), see Motsa [20]. In principle of the SLLM algorithm is to linearize and decouple the system of equations.…”

“…Nonetheless, this method has only been used in a limited number of studies, hence its general validation in complex systems remains to be made. For the interested reader, the SLLM algorithm is described in [20].…”

“…The objective is to extend the study by Nandy [5] to include an evaluation of the impact and significance of thermophoresis and Brownian motion when the nanofluid particle volume fraction at the boundary is not actively controlled. The conservation equations are solved numerically using the spectral local linearization method, see Motsa [20,21]. To show the accuracy of the numerical scheme, analysis of the residual errors is given for different physical parameter values.…”

Impulsive nanofluid flow along a vertical stretching cone

“…Eqs. (9) - (11) are linearized using the Gauss-Seidel approach (see Motsa [28]). The principle of the SLLM algorithm is to linearize and decouple the system of equations.…”

“…Nonetheless, this method has only been used in a limited number of studies, hence its general validation in complex systems remains to be made. The detail derivation of SLLM algorithm is described in [28].…”