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Two complementary lattice-Boltzmann-based analyses for nonlinear systems

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  • 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
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    References listed on IDEAS

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    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.
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    2. 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.
    3. 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.
    4. 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).
    5. 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.

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