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An Asymptotically Adaptive Successive Equilibrium Relaxation approach for the accelerated convergence of the Lattice Boltzmann Method

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  • Boraey, Mohammed A.

Abstract

A new approach is proposed to accelerate the convergence of the Lattice Boltzmann method for steady-state problems. The proposed approach uses an adaptive relaxation frequency to accelerate the convergence by assigning more weight to selected parts of the standard algorithm corresponding to different phases of the convergence to the steady-state solution. The proposed algorithm is simple, straightforward and does not impose any additional computational cost to the standard algorithm. Different simulation cases are presented with the corresponding speedup. Finally, guidelines for the selection of the optimal adaptation parameters are presented.

Suggested Citation

  • Boraey, Mohammed A., 2019. "An Asymptotically Adaptive Successive Equilibrium Relaxation approach for the accelerated convergence of the Lattice Boltzmann Method," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 29-41.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:29-41
    DOI: 10.1016/j.amc.2019.01.061
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    References listed on IDEAS

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    1. David R. Noble & David J. Holdych, 2007. "Full Newton Lattice Boltzmann Method For Time-Steady Flows Using A Direct Linear Solver," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 652-660.
    2. A. M. Artoli & A. G. Hoekstra & P. M. A. Sloot, 2003. "Accelerated Lattice Bgk Method For Unsteady Simulations Through Mach Number Annealing," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 835-845.
    3. Massimo Bernaschi & Sauro Succi & Hudong Chen & Raoyang Zhang, 2002. "Computing Steady State Flows With An Accelerated Lattice Boltzmann Technique," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 675-687.
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    Cited by:

    1. Tao, Shi & He, Qing & Wang, Liang & Chen, Baiman & Chen, Jiechao & Lin, Yousheng, 2021. "Discrete unified gas kinetic scheme simulation of conjugate heat transfer problems in complex geometries by a ghost-cell interface method," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    2. Yeoh, Chin Vern & Ooi, Ean Hin & Foo, Ji Jinn, 2021. "Utilization of pressure wave-dynamics in accelerating convergence of the lattice-Boltzmann method for steady and unsteady flows," Applied Mathematics and Computation, Elsevier, vol. 411(C).

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    1. Yeoh, Chin Vern & Ooi, Ean Hin & Foo, Ji Jinn, 2021. "Utilization of pressure wave-dynamics in accelerating convergence of the lattice-Boltzmann method for steady and unsteady flows," Applied Mathematics and Computation, Elsevier, vol. 411(C).

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