Comparative study of some spectral based methods for solving boundary layer flow problems

2020 ◽  
Author(s):  
Olumuyiwa Otegbeye ◽  
Sicelo P. Goqo ◽  
Md Sharifuddin Ansari
Keyword(s):  
Boundary Layer ◽  
Comparative Study ◽  
Boundary Layer Flow ◽  
Flow Problems ◽  
Layer Flow

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

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
S. S. Motsa
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Nonlinear Boundary ◽  
Linearization Method ◽  
Variable Boundary ◽  
Flow Problems ◽  
Local Linearization ◽  
Highly Nonlinear ◽  
Layer Flow ◽  
Local Linearization Method

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.

scholarly journals Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
P. G. Dlamini ◽  
S. S. Motsa ◽  
M. Khumalo
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Nonlinear Partial Differential Equations ◽  
Finite Difference Schemes ◽  
Unsteady Boundary Layer ◽  
Compact Finite Difference ◽  
Flow Problems ◽  
Layer Flow

We investigate the applicability of the compact finite difference relaxation method (CFDRM) in solving unsteady boundary layer flow problems modelled by nonlinear partial differential equations. The CFDRM utilizes the Gauss-Seidel approach of decoupling algebraic equations to linearize the governing equations and solve the resulting system of ordinary differential equations using compact finite difference schemes. The CFDRM has only been used to solve ordinary differential equations modelling boundary layer problems. This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. The CFDRM is validated on two examples and the results are compared to results of the Keller-box method.

A third-order accurate in time method for boundary layer flow problems

2021 ◽  
Vol 161 ◽  
pp. 13-26 ◽  
Author(s):  
Syed Ahmed Pasha ◽  
Yasir Nawaz ◽  
Muhammad Shoaib Arif
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Third Order ◽  
Flow Problems ◽  
Layer Flow

scholarly journals Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
S. S. Motsa ◽  
P. G. Dlamini ◽  
M. Khumalo
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Relaxation Method ◽  
Nonlinear Pdes ◽  
Quasilinearization Method ◽  
Unsteady Boundary Layer ◽  
Flow Problems ◽  
Spectral Relaxation Method ◽  
Layer Flow ◽  
Spectral Relaxation

Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the methods are more efficient in terms of computational accuracy and speed compared with the Keller-box.

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