Solution of boundary eigenvalue problems and IBVP involving a system of PDEs using the successive linearization method

The paper illustrates a numerical technique to solve a system of three partial differential equations that govern the problem of Rayleigh‐Bénard‐Brinkman convection in a two‐dimensional porous rectangular box. As a result of linear and weakly nonlinear stability analyses of the system a boundary eig...

Full description

Saved in:
Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Mechanik Vol. 103; no. 12
Main Authors: Narayana, M., Siddheshwar, P. G.
Format: Journal Article
Language:English
Published: Weinheim Wiley Subscription Services, Inc 01.12.2023
Subjects:
Boundary value problems
Convection cells
Eigenvalues
Linearization
Matlab
Partial differential equations
Spatial data
Stability analysis
ISSN:0044-2267, 1521-4001
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The paper illustrates a numerical technique to solve a system of three partial differential equations that govern the problem of Rayleigh‐Bénard‐Brinkman convection in a two‐dimensional porous rectangular box. As a result of linear and weakly nonlinear stability analyses of the system a boundary eigenvalue problem (BEVP) and an initial boundary value problem (IBVP) arise. Spatial information on the periodicity of the convection cells is first used in the system of PDEs to make it possible for the successive linearization method (SLM) to be applied. The resulting much‐simplified versions of BEVP and the IVP are then solved by direct and time multi‐stepping versions of SLM, respectively. The SLM solution of the BEVP is compared with that obtained through MATLAB routine bvp4c and the multi‐stepping‐SLM solution of the IVP is validated with that of the Runge‐Kutta‐Fehlberg (RKF45) method (using MATLAB routine ode45). The present numerical technique is found to have quadratic convergence for any desired accuracy. The paper illustrates a numerical technique to solve a system of three partial differential equations that govern the problem of Rayleigh‐Bénard‐Brinkman convection in a two‐dimensional porous rectangular box. As a result of linear and weakly nonlinear stability analyses of the system a boundary eigenvalue problem (BEVP) and an initial boundary value problem (IBVP) arise. Spatial information on the periodicity of the convection cells is first used in the system of PDEs to make it possible for the successive linearization method (SLM) to be applied.…
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.202200472