Lattice Boltzmann model for the volume-averaged Navier-Stokes equations
1 The EMMS Group, State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences - Beijing 100190, China
2 Department of Applied Mathematics, Northwestern Polytechnical University - Xi'an 710129, China
Received: 9 April 2014
Accepted: 24 June 2014
A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged Navier-Stokes equations can be recovered from the lattice Boltzmann equation in the limit of small Mach number by the Chapman-Enskog analysis and Taylor expansion. Due to its advantages such as explicit solver and inherent parallelism, the method appears to be more competitive with traditional numerical techniques. Numerical simulations show that the proposed model can accurately reproduce both the linear and nonlinear drag effects of porosity in the fluid flow through porous media.
PACS: 02.70.-c – Computational techniques; simulations / 05.10.-a – Computational methods in statistical physics and nonlinear dynamics / 47.11.Qr – Lattice gas
© EPLA, 2014