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A novel lattice Boltzmann model for the coupled viscous Burgers’ equations

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  • Li, Qianhuan
  • Chai, Zhenhua
  • Shi, Baochang

Abstract

In this work, a new lattice Boltzmann model for coupled Burgers’ equations is proposed through selecting proper distribution functions. Unlike the previous models, the present model can exactly recover the coupled equations without any assumptions. A detailed numerical study on several coupled Burgers’ equations is performed to validate the present model, and the results show that the present model not only has a second-order convergence rate in space, but also is more accurate than the previous model.

Suggested Citation

  • Li, Qianhuan & Chai, Zhenhua & Shi, Baochang, 2015. "A novel lattice Boltzmann model for the coupled viscous Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 948-957.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:948-957
    DOI: 10.1016/j.amc.2014.11.036
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    References listed on IDEAS

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    1. Chai, Zhenhua & Shi, Baochang & Zheng, Lin, 2008. "A unified lattice Boltzmann model for some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 874-882.
    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. Soliman, A.A., 2006. "The modified extended tanh-function method for solving Burgers-type equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 394-404.
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    2. 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).

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