IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v356y2019icp362-378.html
   My bibliography  Save this article

Moving least squares particle hydrodynamics method for Burgers’ equation

Author

Listed:
  • Fu, Fangyan
  • Li, Jiao
  • Lin, Jun
  • Guan, Yanjin
  • Gao, Fuzheng
  • Zhang, Cunsheng
  • Chen, Liang

Abstract

In this paper, a meshless method named Moving Least Squares Particle Hydrodynamics (MLSPH) method is applied to obtain numerical solutions of the Burgers’ equation with a set of initial and boundary conditions. The influence of kernel function and smoothing length on the accuracy of MLSPH method is investigated. Several various forms of one- and two- dimensional Burgers’ equations are successfully calculated. It is concluded that the proposed method can obtain second-order accuracy. The way of non-uniform distribution is applied to present the desired performance near the shocks. The numerical results obtained by the proposed method are compared with the analytical solutions and the results obtained by some other methods. The satisfactorily small errors indicate the high precision of the proposed method to solve this kind of partial differential equation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:356:y:2019:i:c:p:362-378
    DOI: 10.1016/j.amc.2019.03.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319302474
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.03.040?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. 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.
    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. 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).
    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.
    3. 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.
    4. 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:apmaco:v:356:y:2019:i:c:p:362-378. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.