Comparative Review on Computational Performance of Multistep Schemes in Solving One-Dimensional Linear Wave Equation

Authors

  • Serdar Hayytov Department of Mechanical Engineering, Faculty of Engineering, UCSI University, Kuala Lumpur, Malaysia
  • Wah Yen Tey Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia, Kuala Lumpur, Malaysia https://orcid.org/0000-0002-1865-9212
  • Hooi Siang Kang Marine Technology Center, School of Mechanical Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, Malaysia
  • Mohammed W. Muhieldeen Department of Mechanical Engineering, Faculty of Engineering, UCSI University, Kuala Lumpur, Malaysia
  • Omid Afshar School of Engineering & ICT, University of Tasmania, Australia

DOI:

https://doi.org/10.37934/cfdl.13.6.114

Keywords:

Wave equation, Multistep method, Computational performance

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.

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Published

2021-06-13

How to Cite

Hayytov, S., Tey, W. Y., Kang, H. S., Muhieldeen, M. W., & Afshar, O. (2021). Comparative Review on Computational Performance of Multistep Schemes in Solving One-Dimensional Linear Wave Equation. CFD Letters, 13(6), 1–14. https://doi.org/10.37934/cfdl.13.6.114

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