TY - JOUR

T1 - On the stability of lattice boltzmann equations for one-dimensional diffusion equation

AU - Кривовичев, Герасим Владимирович

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - diffusion

KW - Lattice Boltzmann method

KW - stability

M3 - Article

VL - 8

SP - 1750013-1 -- 1750013-13

JO - International Journal of Modeling, Simulation, and Scientific Computing

JF - International Journal of Modeling, Simulation, and Scientific Computing

SN - 1793-9623

IS - 1

ER -