On the Stability of the Finite Difference based Lattice Boltzmann Method

M.F. El-Amin, S. Sun, A. Salama
2013 Procedia Computer Science  
This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar-Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability
more » ... alysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
doi:10.1016/j.procs.2013.05.380 fatcat:azw6mzwwtjdb5l5c4hz5wr4cou