Preconditioned lattice Boltzmann method for steady flows: A noncascaded central-moments-based approach

2017 ◽  
Vol 96 (6) ◽  
Author(s):  
Alessandro De Rosis
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Steady Flows ◽  
Central Moments ◽  
Boltzmann Method

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

2007 ◽  
Vol 18 (04) ◽  
pp. 652-660 ◽  
Author(s):  
DAVID R. NOBLE ◽  
DAVID J. HOLDYCH
Keyword(s):  
Lattice Boltzmann Method ◽  
Stokes Flow ◽  
Lattice Boltzmann ◽  
Linear Equations ◽  
Steady Flows ◽  
Linear System Of Equations ◽  
Flow Limit ◽  
Non Linear ◽  
Two Dimensional Flow ◽  
Boltzmann Method

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 resolution 251×251, the proposed method performs more than 100 times faster than a standard, fully explicit implementation.

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