"Stability of three-layer finite difference-based lattice Boltzmann schemes"
Krivovichev G.V. and Mikheev S.A.

Stability of three-layer finite difference-based lattice Boltzmann schemes is studied. The time derivative is approximated by the central difference. The stability analysis with respect to initial conditions is performed. The Neumann method is used. It is shown that the stability of the schemes can be improved by the usage of averages of distribution function values on the nearest time layers. It is also shown that the usage of special approximations for the convective terms in the kinetic equations allows one to increase the stability domains in comparison with the case of the schemes with separate approximations of spatial derivatives.

Keywords: lattice Boltzmann method, lattice Boltzmann schemes, stability with respect to initial conditions, Neumann method.

  • Krivovichev G.V. – Saint Petersburg State University, Faculty of Applied Mathematics and Control Processes; prospekt Universitetskii 35, Saint Petersburg, 198504, Russia; Associate Professor, e-mail: gera1983k@bk.ru
  • Mikheev S.A. – Saint Petersburg State University, Faculty of Applied Mathematics and Control Processes; prospekt Universitetskii 35, Saint Petersburg, 198504, Russia; Student, e-mail: helps2@rambler.ru