A Nonlinearly Preconditioned Inexact Newton Algorithm for Steady State Lattice Boltzmann Equations

2016 ◽  
Vol 38 (3) ◽  
pp. A1701-A1724 ◽  
Author(s):  
Jizu Huang ◽  
Chao Yang ◽  
Xiao-Chuan Cai
Keyword(s):  
Steady State ◽  
Lattice Boltzmann ◽  
Boltzmann Equations ◽  
Newton Algorithm ◽  
Lattice Boltzmann Equations

On the stability of lattice boltzmann equations for one-dimensional diffusion equation

2017 ◽  
Vol 08 (01) ◽  
pp. 1750013 ◽  
Author(s):  
Gerasim Vladimirovich Krivovichev
Keyword(s):  
Lattice Boltzmann ◽  
Initial Conditions ◽  
Kinetic Equations ◽  
Differential Approximation ◽  
Boltzmann Equations ◽  
Von Neumann ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
The Cauchy Problem ◽  
Lattice Boltzmann Equations

Stability analysis of lattice Boltzmann equations (LBEs) on initial conditions for one-dimensional diffusion is performed. Stability of the solution of the Cauchy problem for the system of linear Bhatnaghar–Gross–Krook kinetic equations is demonstrated for the cases of D1Q2 and D1Q3 lattices. Stability of the scheme for D1Q2 lattice is analytically analyzed by the method of differential approximation. Stability of parametrical scheme is numerically investigated by von Neumann method in parameter space. As a result of numerical analysis, the correction of the hypothesis on transfer of stability conditions of the scheme for macroequation to the system of LBEs is demonstrated.

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