Investigation of the stability of explicit finite difference-based lattice Boltzmann schemes

Authors

  • G.V. Krivovichev

Keywords:

kinetic schemes
lattice Boltzmann equation
finite difference-based lattice Boltzmann schemes
stability with respect to initial conditions
Neumann method
stability domain

Abstract

The stability problem is considered for finite difference-based lattice Boltzmann kinetic schemes for simulating the plane flows of a viscous incompressible isothermal fluid. Stability is studied for two steady modes of flow in an unbounded domain. The stability analysis is performed with respect to initial conditions using the Neumann method in a linear approximation. A number of stability domains are constructed and studied in the space of input parameters. It is shown that the schemes under consideration are conditionally stable. It is demonstrated that the stability domains for a scheme with the first order upwind differences are included the maximum amount of points in a wide range of input parameters. It is shown for the case of equal time and space grid steps that the areas of the stability domains for the lattice Boltzmann equation are larger than for the cases of finite difference-based schemes.

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Published

2012-05-22

Issue

Vol. 13 (2012): Issue 2.

Section

Section 1. Numerical methods and applications

Author Biography

G.V. Krivovichev

St Petersburg University,
Faculty of Applied Mathematics and Control Processes
Universitetskii prospekt 35, Petergof, Saint Petersburg, 198504, Russia
• Associate Professor

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