Mathematics and Statistics Vol. 11(2), pp. 277 - 287
DOI: 10.13189/ms.2023.110205
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A Rotated Similarity Reduction Approach with Half-Sweep Successive Over-Relaxation Iteration for Solving Two-Dimensional Unsteady Convection-Diffusion Problems

Nur Afza Mat Ali ¹, Jumat Sulaiman ^1,2,*, Azali Saudi ³, Nor Syahida Mohamad ^1
1 Faculty of Science and Natural Resources, Universiti Malaysia Sabah, 88400, Kota Kinabalu, Sabah, Malaysia
² Preparatory Centre for Science and Technology, Universiti Malaysia Sabah, 88400, Kota Kinabalu, Sabah, Malaysia
³ Faculty of Computing and Informatics, Universiti Malaysia Sabah, 88400, Kota Kinabalu, Sabah, Malaysia

ABSTRACT

In this paper, we transformed a two-dimensional unsteady convection-diffusion equation into a two-dimensional steady convection-diffusion equation using the similarity transformation technique. This technique can be easily applied to linear or nonlinear problems and is capable of reducing the size of computational works since the main idea of this technique is to reduce at least one independent variable. The corresponding similarity equation is then solved numerically using an effective numerical technique, namely a new five-point rotated similarity finite difference scheme via half-sweep successive over-relaxation iteration. This work compared the performance of the proposed method with Gauss-Seidel and successive over-relaxation with the full-sweep concept. Numerical tests were carried out to obtain the performance of the proposed method using C simulation. The results revealed that the combination of the five-point rotated similarity finite difference scheme via half-sweep successive over-relaxation iteration is the most superior method in terms of the iteration number and computational time compared to all these methods. Additionally, in terms of accuracy, all three iterative methods are also comparable.

KEYWORDS
Partial Differential Equation, Similarity Solution, Similarity Rotated Finite Difference Scheme, Half-Sweep Weighted Iteration

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Nur Afza Mat Ali , Jumat Sulaiman , Azali Saudi , Nor Syahida Mohamad , "A Rotated Similarity Reduction Approach with Half-Sweep Successive Over-Relaxation Iteration for Solving Two-Dimensional Unsteady Convection-Diffusion Problems," Mathematics and Statistics, Vol. 11, No. 2, pp. 277 - 287, 2023. DOI: 10.13189/ms.2023.110205.

(b). APA Format:
Nur Afza Mat Ali , Jumat Sulaiman , Azali Saudi , Nor Syahida Mohamad (2023). A Rotated Similarity Reduction Approach with Half-Sweep Successive Over-Relaxation Iteration for Solving Two-Dimensional Unsteady Convection-Diffusion Problems. Mathematics and Statistics, 11(2), 277 - 287. DOI: 10.13189/ms.2023.110205.