IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v486y2017icp1000-1011.html
   My bibliography  Save this article

Two complementary lattice-Boltzmann-based analyses for nonlinear systems

Author

Listed:
  • Otomo, Hiroshi
  • Boghosian, Bruce M.
  • Dubois, François

Abstract

Lattice Boltzmann models that asymptotically reproduce solutions of nonlinear systems are derived by the Chapman–Enskog method and the analytic method based on recursive substitution and Taylor-series expansion. While both approaches yield identical hydrodynamic equations and can be generalized to analyze a variety of nonlinear systems, they have complementary advantages and disadvantages. In particular, the error analysis is substantially easier using the Taylor-series expansion method. In this work, the Burgers’, Korteweg–de Vries, and Kuramoto–Sivashinsky equations are analyzed using both approaches, and the results are discussed and compared with analytic solutions and previous studies.

Suggested Citation

  • Otomo, Hiroshi & Boghosian, Bruce M. & Dubois, François, 2017. "Two complementary lattice-Boltzmann-based analyses for nonlinear systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 1000-1011.
    • Handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:1000-1011
    DOI: 10.1016/j.physa.2017.06.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117306490
    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.2017.06.010?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. Lai, Huilin & Ma, Changfeng, 2009. "Lattice Boltzmann method for the generalized Kuramoto–Sivashinsky equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1405-1412.
    2. Yan, Guangwu & Zhang, Jianying, 2009. "A higher-order moment method of the lattice Boltzmann model for the Korteweg–de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1554-1565.
    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. Ahmadi Balootaki, Azam & Karimipour, Arash & Toghraie, Davood, 2018. "Nano scale lattice Boltzmann method to simulate the mixed convection heat transfer of air in a lid-driven cavity with an endothermic obstacle inside," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 681-701.
    2. Karimipour, Arash & D’Orazio, Annunziata & Goodarzi, Marjan, 2018. "Develop the lattice Boltzmann method to simulate the slip velocity and temperature domain of buoyancy forces of FMWCNT nanoparticles in water through a micro flow imposed to the specified heat flux," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 729-745.
    3. Goodarzi, Marjan & D’Orazio, Annunziata & Keshavarzi, Ahmad & Mousavi, Sayedali & Karimipour, Arash, 2018. "Develop the nano scale method of lattice Boltzmann to predict the fluid flow and heat transfer of air in the inclined lid driven cavity with a large heat source inside, Two case studies: Pure natural ," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 210-233.
    4. Safaei, Mohammad Reza & Karimipour, Arash & Abdollahi, Ali & Nguyen, Truong Khang, 2018. "The investigation of thermal radiation and free convection heat transfer mechanisms of nanofluid inside a shallow cavity by lattice Boltzmann method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 515-535.
    5. Baty, Hubert & Drui, Florence & Helluy, Philippe & Franck, Emmanuel & Klingenberg, Christian & Thanhäuser, Lukas, 2023. "A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations," Applied Mathematics and Computation, Elsevier, vol. 440(C).

    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. Che Sidik, Nor Azwadi & Aisyah Razali, Siti, 2014. "Lattice Boltzmann method for convective heat transfer of nanofluids – A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 38(C), pages 864-875.
    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. Zhang, Xiaohua & Zhang, Ping, 2018. "A reduced high-order compact finite difference scheme based on proper orthogonal decomposition technique for KdV equation," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 535-545.
    4. Kaur, Navneet & Joshi, Varun, 2024. "Kuramoto-Sivashinsky equation: Numerical solution using two quintic B-splines and differential quadrature method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 105-127.
    5. 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.
    6. Duan, Yali & Kong, Linghua & Zhang, Rui, 2012. "A lattice Boltzmann model for the generalized Burgers–Huxley equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 625-632.
    7. Bakhshan, Younes & Omidvar, Alireza, 2015. "Calculation of friction coefficient and analysis of fluid flow in a stepped micro-channel for wide range of Knudsen number using Lattice Boltzmann (MRT) method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 440(C), pages 161-175.
    8. Liu, Qing & He, Ya-Ling, 2015. "Double multiple-relaxation-time lattice Boltzmann model for solid–liquid phase change with natural convection in porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 94-106.
    9. Du, Rui & Sun, Dongke & Shi, Baochang & Chai, Zhenhua, 2019. "Lattice Boltzmann model for time sub-diffusion equation in Caputo sense," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 80-90.

    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:486:y:2017:i:c:p:1000-1011. 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.