IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v196y2022icp151-165.html
   My bibliography  Save this article

High-order implicit weighted compact nonlinear scheme for nonlinear coupled viscous Burgers’ equations

Author

Listed:
  • Zhang, Xu
  • Jiang, Yanqun
  • Hu, Yinggang
  • Chen, Xun

Abstract

In this paper a high-order implicit weighted compact nonlinear scheme for nonlinear coupled viscous Burgers’ equations is presented. The fifth-order weighted compact nonlinear scheme is used for the spatial discretization, while the third-order diagonal implicit Runge–Kutta method is used for the time discretization. The generated nonlinear system is solved by the Jacobian-free Newton–Krylov nonlinear solver, which is composed of the outer Newton iteration method and the inner Krylov subspace iteration method. Stability analysis shows that the presented implicit weighted compact nonlinear scheme is unconditionally stable. Numerical results indicate that the implicit scheme can achieve the designed third-order accuracy in time and has a great advantage in the computation efficiency compared to the third-order explicit total variation diminishing Runge–Kutta weighted essentially non-oscillatory scheme. In addition, the implicit scheme can capture discontinuities and shock waves with high resolution and can solve Burgers’ equations with all kinds of Reynolds numbers.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:151-165
    DOI: 10.1016/j.matcom.2022.01.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847542200009X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2022.01.009?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. 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.
    2. Guo, Yan & Shi, Yu-feng & Li, Yi-min, 2016. "A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 172-185.
    3. Botti, L., 2015. "A choice of forcing terms in inexact Newton iterations with application to pseudo-transient continuation for incompressible fluid flow computations," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 713-737.
    4. Jiang, Yanqun & Chen, Xun & Fan, Rong & Zhang, Xu, 2021. "High order semi-implicit weighted compact nonlinear scheme for viscous Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 607-621.
    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. 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).
    7. Zhao, Guoyan & Sun, Mingbo & Xie, Songbai & Wang, Hongbo, 2018. "Numerical dissipation control in an adaptive WCNS with a new smoothness indicator," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 239-253.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Park, Sangbeom & Jeon, Yonghyeon & Kim, Philsu & Bak, Soyoon, 2024. "An error predict-correction formula of the load vector in the BSLM for solving three-dimensional Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 222-243.
    2. Kaushik, Sonali & Kumar, Rajesh, 2023. "Optimized decomposition method for solving multi-dimensional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 326-350.

    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. Kaennakham, S. & Chuathong, N., 2019. "An automatic node-adaptive scheme applied with a RBF-collocation meshless method," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 102-125.
    3. Li, Wenjuan & Gao, Fuzheng & Cui, Jintao, 2024. "A weak Galerkin finite element method for nonlinear convection-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 461(C).
    4. Kaushik, Sonali & Kumar, Rajesh, 2023. "Optimized decomposition method for solving multi-dimensional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 326-350.
    5. Veeresha, P. & Prakasha, D.G., 2019. "A novel technique for (2+1)-dimensional time-fractional coupled Burgers equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 324-345.
    6. Zhang, Huaibao & Zhang, Fan & Xu, Chunguang, 2019. "Towards optimal high-order compact schemes for simulating compressible flows," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 221-237.
    7. Fu, Fangyan & Li, Jiao & Lin, Jun & Guan, Yanjin & Gao, Fuzheng & Zhang, Cunsheng & Chen, Liang, 2019. "Moving least squares particle hydrodynamics method for Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 362-378.
    8. 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.
    9. Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
    10. 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).
    11. Noufe H. Aljahdaly & Ravi P. Agarwal & Rasool Shah & Thongchai Botmart, 2021. "Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators," Mathematics, MDPI, vol. 9(18), pages 1-24, September.
    12. Cavoretto, Roberto, 2022. "Adaptive LOOCV-based kernel methods for solving time-dependent BVPs," Applied Mathematics and Computation, Elsevier, vol. 429(C).

    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:matcom:v:196:y:2022:i:c:p:151-165. 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/mathematics-and-computers-in-simulation/ .

    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.