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Full Newton Lattice Boltzmann Method For Time-Steady Flows Using A Direct Linear Solver

Author

Listed:
  • DAVID R. NOBLE

    (Multiphase Transport Processes, Sandia National Laboratories, MS-0834, P.O. Box 5800, Albuquerque, NM 87185-0834, USA)

  • DAVID J. HOLDYCH

    (Microscale Science and Technology, Sandia National Laboratories, MS-0826, P.O. Box 5800, Albuquerque, NM 87185-0826, USA)

Abstract

A full Newton lattice Boltzmann method is developed for time-steady flows. The general method involves the construction of a residual form for the time-steady, nonlinear Boltzmann equation in terms of the probability distribution. Bounce-back boundary conditions are also incorporated into the residual form. Newton's method is employed to solve the resulting system of non-linear equations. At each Newton iteration, the sparse, banded, Jacobian matrix is formed from the dependencies of the non-linear residuals on the components of the particle distribution. The resulting linear system of equations is solved using a direct solver designed for sparse, banded matrices. For the Stokes flow limit, only one matrix solve is required. Two dimensional flow about a periodic array of disks is simulated as a proof of principle, and the numerical efficiency is carefully assessed. For the case of Stokes flow(Re = 0)with resolution251×251, the proposed method performs more than 100 times faster than a standard, fully explicit implementation.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:04:n:s0129183107010905
    DOI: 10.1142/S0129183107010905
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    Cited by:

    1. 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.

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