IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v309y2017icp334-349.html
   My bibliography  Save this article

Finite-difference lattice Boltzmann model for nonlinear convection-diffusion equations

Author

Listed:
  • Wang, Huili
  • Shi, Baochang
  • Liang, Hong
  • Chai, Zhenhua

Abstract

In this paper, a finite-difference lattice Boltzmann (LB) model for nonlinear isotropic and anisotropic convection-diffusion equations is proposed. In this model, the equilibrium distribution function is delicately designed in order to recover the convection-diffusion equation exactly. Different from the standard LB model, the temporal and spatial steps in this model are decoupled such that it is convenient to study convection-diffusion problem with the non-uniform grid. In addition, it also preserves the advantage of standard LB model that the complex-valued convection-diffusion equation can be solved directly. The von Neumann stability analysis is conducted to discuss the stability region which can be used to determine the free parameters appeared in the model. To test the performance of the model, a series of numerical simulations of some classical problems, including the diffusion equation, the nonlinear heat conduction equation, the Sine-Gordon equation, the Gaussian hill problem, the Burgers–Fisher equation, and the nonlinear Schrödinger equation, have also been carried out. The results show that the present model has a second-order convergence rate in space, and generally it is also more accurate than the standard LB model.

Suggested Citation

  • Wang, Huili & Shi, Baochang & Liang, Hong & Chai, Zhenhua, 2017. "Finite-difference lattice Boltzmann model for nonlinear convection-diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 334-349.
  • Handle: RePEc:eee:apmaco:v:309:y:2017:i:c:p:334-349
    DOI: 10.1016/j.amc.2017.04.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031730259X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2017.04.015?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. Sheng, Q. & Khaliq, A.Q. M. & Voss, D.A., 2005. "Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(4), pages 355-373.
    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. 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.
    2. Cheichan, Mohammed S. & Kashkool, Hashim A. & Gao, Fuzheng, 2019. "A weak Galerkin finite element method for solving nonlinear convection-diffusion problems in two dimensions," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 149-163.

    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. Adak, D. & Natarajan, S., 2020. "Virtual element method for semilinear sine–Gordon equation over polygonal mesh using product approximation technique," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 224-243.
    2. Almushaira, Mustafa, 2023. "Efficient energy-preserving eighth-order compact finite difference schemes for the sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    3. Dehghan, Mehdi & Shokri, Ali, 2008. "A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 700-715.
    4. Hu, Dongdong & Cai, Wenjun & Xu, Zhuangzhi & Bo, Yonghui & Wang, Yushun, 2021. "Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine–Gordon equation with damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 35-59.
    5. Jiang, Chaolong & Sun, Jianqiang & Li, Haochen & Wang, Yifan, 2017. "A fourth-order AVF method for the numerical integration of sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 144-158.

    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:309:y:2017:i:c:p:334-349. 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.