On the stability of lattice boltzmann equations for one-dimensional diffusion equation-Reference-Cited by-同舟云学术

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

Published:2017-01-10 Issue:01 Volume:08 Page:1750013
ISSN:1793-9623
Container-title:International Journal of Modeling, Simulation, and Scientific Computing
language:en
Short-container-title:Int. J. Model. Simul. Sci. Comput.

Author:

Krivovichev Gerasim Vladimirovich¹^ORCID

Affiliation:

1. Faculty of Applied Mathematics and Processes of Control, Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russian Federation

Abstract

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.

Funder

Russian Foundation for Basic Research

Publisher

World Scientific Pub Co Pte Lt

Subject

Computer Science Applications,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793962317500131

Reference25 articles.

1. LATTICE BOLTZMANN METHOD FOR FLUID FLOWS

2. The lattice Boltzmann equation method: theoretical interpretation, numerics and implications

3. A higher-order moment method of the lattice Boltzmann model for the Korteweg–de Vries equation

4. A New Lattice Boltzmann Model for KdV-Burgers Equation

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