Analysis and optimization of higher order explicit finite-difference schemes for the advection stage implementation in the lattice Boltzmann method
G. V. Krivovichev, E. S. Marnopolskaya
St. Petersburg State University, Faculty of Applied Mathematics and Control Processes
This paper is devoted to the analysis and optimization of explicit finite-difference
schemes for solving the transport equations arising at the advection stage in
the method of splitting into physical processes. The method can be applied to the
lattice Boltzmann equations and to the kinetic equations of general type. The
second-to-fourth order schemes are considered. In order to minimize the effect
of numerical dispersion and dissipation, the parametric schemes are used.
The Neumann method and the polynomial approximation of the boundaries of stability
domains are employed to obtain the stability conditions in the form of inequalities
imposed on the Courant parameter. The optimal values of the parameter used to
control the dissipation and dispersion effects are found by minimizing the
maximum function. The schemes with optimal parameters are applied for the numerical
solution of 1D and 2D advection equations and for the problem of lid-driven cavity flow.
lattice Boltzmann method, splitting method, stability, dispersion, dissipation.
PDF file (841 kB)
G. V. Krivovichev, E. S. Marnopolskaya, “Analysis and optimization of higher order explicit finite-difference schemes for the advection stage implementation in the lattice Boltzmann method”, Num. Meth. Prog., 18:3 (2017), 227–246
Citation in format AMSBIB
\by G.~V.~Krivovichev, E.~S.~Marnopolskaya
\paper Analysis and optimization of higher order explicit finite-difference schemes for the advection stage implementation in the lattice Boltzmann method
\jour Num. Meth. Prog.
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