Comparative review on computational performance of multistep schemes in solving one dimensional linear wave equation

Hayytov, Serdar and Tey, Wah Yen and Kang, Hooi Siang and Muhieldeen, Mohammed W. and Afshar, Omid (2021) Comparative review on computational performance of multistep schemes in solving one dimensional linear wave equation. CFD Letters, 13 (6). pp. 1-14. ISSN 2180-1363

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Official URL: http://dx.doi.org/10.37934/cfdl.13.6.114

Abstract

Among several numerical methods used to solve the hyperbolic model of the linear wave equation, single-step algorithms can be the more popular ones. However, these algorithms are time-consuming while incurring numerical inaccuracy. Thus, multistep methods can be a suitable option as it has a high order of accuracy. This study aims to investigate and compare the computational performance of these multistep schemes in solving hyperbolic model based on one-dimensional linear wave equation. The techniques studied in this paper comprise the two-step Lax-Wendroff method, MacCormack method, second-order upwind method, Rusanov-Burstein-Mirin method, Warming-Kutler-Lomax method, and fourth-order Runge-Kutta method. Finite difference method is applied in discretisation. Our simulation found that although higher-order multistep methods are more stable than single-step algorithm, they suffer numerical diffusion. The two-step Lax-Wendroff method outperforms other schemes, although it is relatively simple compared with the other three and four steps schemes. The second-order upwind method is attractive as well because it is executable even with a high Courant number.

Item Type:Article
Uncontrolled Keywords:computational performance, multistep method, wave equation
Subjects:Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
Divisions:Malaysia-Japan International Institute of Technology
ID Code:95851
Deposited By: Yanti Mohd Shah
Deposited On:20 Jun 2022 16:48
Last Modified:20 Jun 2022 16:48

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