Application of lattice kinetic models with Tsallis entropy in simulating fluid flow through porous media

In this work, application of the recently introduced constant speed kinetic model (CSKM) [A. Zadehgol and M. Ashrafizaadeh, J. Comp. Phys. 274 803, (2014); A. Zadehgol, Phys. Rev. E 91, 063311 (2015)] in simulating fluid flow through porous media is explored. Discrete forms of Tsallis and Burg entropy functions were first introduced by Boghosian et al. [Phys. Rev. E 68, 025103, (2003)], in the context of lattice Boltzmann model (LBM). In the CSKM, the virtual particles are concentrated on n-dimensional (nD-) spheres centered at the computational nodes. Using continuous forms of the unconventional entropies of Burg, h similar to log f (for 2D), and Tsallis, h similar to f(1-2/n) (for nD with n >= 3), the CSKM extends the work of Boghosian et al., in the limit of fixed speed continuous velocities. In this work, the second-order accuracy, effciency, and thermodynamic consistency of the 2D- and 3D-projections of the 4D-CSKM are explored and numerically verified.