FULL NEWTON LATTICE BOLTZMANN METHOD FOR TIME-STEADY FLOWS USING A DIRECT LINEAR SOLVER

David R. Noble () and David J. Holdych ()
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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

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 04, 652-660

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.

Keywords: Lattice Boltzmann; Newton-Raphson; time-steady flows; performance; 11.25.Hf; 123.1K (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183107010905

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