Analysis and optimization of higher order explicit finite-difference schemes for the advection stage implementation in the lattice Boltzmann method

Authors

DOI:

https://doi.org/10.26089/NumMet.v18r321

Keywords:

lattice Boltzmann method, splitting method, stability, dispersion, dissipation

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.

Author Biographies

G.V. Krivovichev

St Petersburg University
• Associate Professor

E.S. Marnopolskaya

St Petersburg University
• Student

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Published

26-06-2017

How to Cite

Кривовичев Г., Марнопольская Е. Analysis and Optimization of Higher Order Explicit Finite-Difference Schemes for the Advection Stage Implementation in the Lattice Boltzmann Method // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2017. 18. 227-246. doi 10.26089/NumMet.v18r321

Issue

Vol. 18 (2017): Issue 3.

Section

Section 1. Numerical methods and applications

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