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A Fourth Order Numerical Scheme for Unsteady Mixed Convection Boundary Layer Flow: A Comparative Computational Study

Author

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  • Yasir Nawaz

    (Department of Mathematics, Air University Islamabad, PAF Complex E-9, Islamabad 44000, Pakistan
    Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad 44000, Pakistan)

  • Muhammad Shoaib Arif

    (Department of Mathematics, Air University Islamabad, PAF Complex E-9, Islamabad 44000, Pakistan
    Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • Wasfi Shatanawi

    (Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan)

  • Muhammad Usman Ashraf

    (Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad 44000, Pakistan)

Abstract

In this paper, a three-stage fourth-order numerical scheme is proposed. The first and second stages of the proposed scheme are explicit, whereas the third stage is implicit. A fourth-order compact scheme is considered to discretize space-involved terms. The stability of the fourth-order scheme in space and time is checked using the von Neumann stability criterion for the scalar case. The stability region obtained by the scheme is more than the one given by explicit Runge–Kutta methods. The convergence conditions are found for the system of partial differential equations, which are non-dimensional equations of heat transfer of Stokes first and second problems. The comparison of the proposed scheme is made with the existing Crank–Nicolson scheme. From this comparison, it can be concluded that the proposed scheme converges faster than the Crank–Nicolson scheme. It also produces less relative error than the Crank–Nicolson method for time-dependent problems.

Suggested Citation

  • Yasir Nawaz & Muhammad Shoaib Arif & Wasfi Shatanawi & Muhammad Usman Ashraf, 2022. "A Fourth Order Numerical Scheme for Unsteady Mixed Convection Boundary Layer Flow: A Comparative Computational Study," Energies, MDPI, vol. 15(3), pages 1-15, January.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:3:p:910-:d:735382
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    References listed on IDEAS

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    1. Yang, Xiaojia & Ge, Yongbin & Zhang, Lin, 2019. "A class of high-order compact difference schemes for solving the Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 394-417.
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    Cited by:

    1. Yasir Nawaz & Muhammad Shoaib Arif & Kamaleldin Abodayeh & Mairaj Bibi, 2022. "Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer," Energies, MDPI, vol. 15(13), pages 1-22, June.
    2. Magdalena Piasecka & Krzysztof Dutkowski, 2022. "Novel Numerical Methods in Heat and Mass Transfer," Energies, MDPI, vol. 15(7), pages 1-3, April.
    3. Yasir Nawaz & Muhammad Shoaib Arif & Wasfi Shatanawi & Mairaj Bibi, 2022. "A New Explicit Numerical Schemes for Time-Dependent PDEs with Application to Pressure Driven Fluid Flow in a Rectangular Duct," Energies, MDPI, vol. 15(14), pages 1-22, July.

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