DOI: https://doi.org/10.26089/NumMet.v16r220

Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation

Authors

  • G.V. Krivovichev
  • S.A. Mikheev

Keywords:

lattice Boltzmann method
lattice Boltzmann schemes
stability with respect to initial conditions
Neumann method

Abstract

The stability of three-level finite-difference-based lattice Boltzmann schemes of third and fourth orders of approximation with respect to spatial variables is studied. The stability analysis with respect to initial conditions is performed on the basis of a linear approximation. These studies are based on the Neumann method. It is shown that the stability of the schemes can be improved by the approximation convective terms in internal nodes of the grid stencils in use. In this case the stability domains are larger compared to the case of approximation in boundary nodes.

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Published

2015-04-20

Issue

Vol. 16 (2015): Issue 2.

Section

Section 1. Numerical methods and applications

Author Biographies

G.V. Krivovichev

St Petersburg University,
Faculty of Applied Mathematics and Control Processes
• Associate Professor

S.A. Mikheev

St Petersburg University,
Faculty of Applied Mathematics and Control Processes
• Student

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