Open AccessPerformance of similarity explicit group iteration for solving 2D unsteady convection-diffusion equation
Author(s) -
Nur Afza Mat Ali,
Jumat Sulaiman,
Azali Saudi,
Nor Syahida Mohamad
Publication year - 2021
Publication title -
indonesian journal of electrical engineering and computer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.241
H-Index - 17
eISSN - 2502-4760
pISSN - 2502-4752
DOI - 10.11591/ijeecs.v23.i1.pp471-478
Subject(s) - mathematics , discretization , similarity (geometry) , partial differential equation , iterative method , numerical solution of the convection–diffusion equation , convection–diffusion equation , diffusion equation , similarity solution , alternating direction implicit method , matrix similarity , finite difference method , mathematical analysis , algorithm , computer science , economy , artificial intelligence , economics , image (mathematics) , service (business) , physics , boundary layer , thermodynamics
In this paper, a similarity finite difference (SFD) solution is addressed for thetwo-dimensional (2D) parabolic partial differential equation (PDE), specifically on the unsteady convection-diffusion problem. Structuring the similarity transformation using wave variables, we reduce the parabolic PDE into elliptic PDE. The numerical solution of the corresponding similarity equation is obtained using a second-order central SFD discretization schemeto get the second-order SFD approximation equation. We propose a four-point similarity explicit group (4-point SEG) iterative methodasa numericalsolution of the large-scale and sparse linear systems derived from SFD discretization of 2D unsteady convection-diffusion equation (CDE). To showthe 4-point SEG iteration efficiency, two iterative methods, such as Jacobiand Gauss-Seidel (GS) iterations, are also considered. The numerical experiments are carried out using three different problems to illustrate our proposed iterative method's performance. Finally, the numerical results showed that our proposed iterative method is more efficient than the Jacobiand GS iterations in terms of iteration number and execution time.