Research output: Contribution to journal › Article
On the stability of lattice boltzmann equations for one-dimensional diffusion equation. / Кривовичев, Герасим Владимирович.
In: International Journal of Modeling, Simulation, and Scientific Computing, Vol. 8, No. 1, 2017, p. 1750013-1 -- 1750013-13.Research output: Contribution to journal › Article
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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 -
ID: 7734476