IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v545y2020ics0378437119320928.html
   My bibliography  Save this article

A numerical treatment of the coupled viscous Burgers’ equation in the presence of very large Reynolds number

Author

Listed:
  • Başhan, Ali

Abstract

A numerical investigation of the coupled viscous Burgers’ equation for very large Reynolds numbers do not exist in the literature. Coupled viscous Burgers’ equations are solved numerically in the presence of very large Reynolds numbers. For this case, numerical approach to the coupled viscous Burgers’ equation via contributions of two effective methods is used. The first component of the mixed method is finite difference method and the second one is differential quadrature method. For this process, the third order modified cubic B-spline functions are used as base function. To display the effectiveness of the present mixed method four different test problems have been investigated. For various values of the coefficients, more particularly for very large Reynolds numbers, in other words, for the very small value of kinematic viscosity parameters solutions are obtained. Error norms are calculated and compared with analytical results and also with numerical results of the related literature. Present results display that the present mixed method obtains high accurate solutions and in compatibility with both of the analytical and numerical results.

Suggested Citation

  • Başhan, Ali, 2020. "A numerical treatment of the coupled viscous Burgers’ equation in the presence of very large Reynolds number," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320928
    DOI: 10.1016/j.physa.2019.123755
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119320928
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123755?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Qianhuan & Chai, Zhenhua & Shi, Baochang, 2015. "A novel lattice Boltzmann model for the coupled viscous Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 948-957.
    2. Lai, Huilin & Ma, Changfeng, 2014. "A new lattice Boltzmann model for solving the coupled viscous Burgers’ equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 445-457.
    3. Soliman, A.A., 2006. "The modified extended tanh-function method for solving Burgers-type equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 394-404.
    4. Ali Başhan & N. Murat Yağmurlu & Yusuf Uçar & Alaattin Esen, 2018. "A new perspective for the numerical solutions of the cmKdV equation via modified cubic B-spline differential quadrature method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-17, June.
    5. Doğan Kaya, 2001. "An explicit solution of coupled viscous Burgers' equation by the decomposition method," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 27, pages 1-6, January.
    6. Mohanty, R.K. & Dai, Weizhong & Han, Fei, 2015. "Compact operator method of accuracy two in time and four in space for the numerical solution of coupled viscous Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 381-393.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Park, Sangbeom & Kim, Philsu & Jeon, Yonghyeon & Bak, Soyoon, 2022. "An economical robust algorithm for solving 1D coupled Burgers’ equations in a semi-Lagrangian framework," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    2. Li, Qianhuan & Chai, Zhenhua & Shi, Baochang, 2015. "A novel lattice Boltzmann model for the coupled viscous Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 948-957.
    3. Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
    4. Attaullah & Muhammad Shakeel & Nehad Ali Shah & Jae Dong Chung, 2022. "Modified Exp-Function Method to Find Exact Solutions of Ionic Currents along Microtubules," Mathematics, MDPI, vol. 10(6), pages 1-10, March.
    5. Kavitha, L. & Prabhu, A. & Gopi, D., 2009. "New exact shape changing solitary solutions of a generalized Hirota equation with nonlinear inhomogeneities," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2322-2329.
    6. Lai, Huilin & Ma, Changfeng, 2014. "A new lattice Boltzmann model for solving the coupled viscous Burgers’ equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 445-457.
    7. Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
    8. Cui Guo & Yinglin Wang & Yuesheng Luo, 2021. "A Conservative and Implicit Second-Order Nonlinear Numerical Scheme for the Rosenau-KdV Equation," Mathematics, MDPI, vol. 9(11), pages 1-15, May.
    9. Soliman, A.A., 2009. "On the solution of two-dimensional coupled Burgers’ equations by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1146-1155.
    10. Cengizci, Süleyman & Uğur, Ömür, 2023. "A stabilized FEM formulation with discontinuity-capturing for solving Burgers’-type equations at high Reynolds numbers," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    11. Mohanty, R.K. & Dai, Weizhong & Han, Fei, 2015. "Compact operator method of accuracy two in time and four in space for the numerical solution of coupled viscous Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 381-393.
    12. Başhan, Ali, 2019. "A mixed algorithm for numerical computation of soliton solutions of the coupled KdV equation: Finite difference method and differential quadrature method," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 42-57.
    13. Chen, Changkai & Zhang, Xiaohua & Liu, Zhang, 2020. "A high-order compact finite difference scheme and precise integration method based on modified Hopf-Cole transformation for numerical simulation of n-dimensional Burgers’ system," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    14. Zhang, Xu & Jiang, Yanqun & Hu, Yinggang & Chen, Xun, 2022. "High-order implicit weighted compact nonlinear scheme for nonlinear coupled viscous Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 151-165.
    15. Krivovichev, Gerasim V., 2018. "Linear Bhatnagar–Gross–Krook equations for simulation of linear diffusion equation by lattice Boltzmann method," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 102-119.
    16. Ali Başhan, 2023. "A novel outlook to the an alternative equation for modelling shallow water wave: Regularised Long Wave (RLW) equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(1), pages 133-145, March.
    17. Başhan, Ali, 2021. "Highly efficient approach to numerical solutions of two different forms of the modified Kawahara equation via contribution of two effective methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 111-125.
    18. Cui, Lijie & Lin, Chuandong, 2021. "A simple and efficient kinetic model for wealth distribution with saving propensity effect: Based on lattice gas automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    19. Goswami, Amit & Singh, Jagdev & Kumar, Devendra & Sushila,, 2019. "An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 563-575.
    20. Abourabia, A.M. & El-Danaf, T.S. & Morad, A.M., 2009. "Exact solutions of the hierarchical Korteweg–de Vries equation of microstructured granular materials," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 716-726.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320928. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.