"Study of properties of a finite-difference scheme for the advection stage implementation in the lattice Boltzmann method"
Krivovichev G.V. and Marnopolskaya E.S.

A finite-difference single-parameter scheme for solving the system of advection equations arising in the application of the method of splitting into physical processes to a system of kinetic equations is studied. The stability analysis is performed using the Neumann method. A stability domain in the "scheme's parameter-Courant number" plane is constructed. It is shown that an appropriate choice of this parameter allows one to regulate the dispersive and dissipative properties of the scheme. An approach of choosing the optimal parameter is proposed on the basis of an optimization of dispersive and dissipative surfaces. An efficiency of the scheme with the optimal parameter is illustrated by the numerical solution of the cavity flow problem and the problem on the propagation of shear waves in viscous fluid.

Keywords: lattice Boltzmann method, splitting into physical processes, advection equation, 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; Ph.D., Associate Professor, e-mail: g.krivovichev@spbu.ru
  • Marnopolskaya E.S. – Saint Petersburg State University, Faculty of Applied Mathematics and Control Processes; prospekt Universitetskii 35, Saint Petersburg, 198504, Russia; Student, e-mail: marnlena@yandex.ru