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Num. Meth. Prog., 2017, Volume 18, Issue 3, Pages 227–246 (Mi vmp876)  

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

Abstract: 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.

Keywords: lattice Boltzmann method, splitting method, stability, dispersion, dissipation.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-00021мол_а


Full text: PDF file (841 kB)
UDC: 519.633
Received: 13.06.2017

Citation: 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
\Bibitem{KriMar17}
\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.
\yr 2017
\vol 18
\issue 3
\pages 227--246
\mathnet{http://mi.mathnet.ru/vmp876}


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