Introducing unsteady non‐uniform source terms into the lattice Boltzmann model

Taking body forces into account is not new for the lattice Boltzmann method, yet most of the existing approaches can only treat steady and uniform body forces. To manage situations with time‐ and space‐dependent body forces or source terms, this paper proposes a new approach through theoretical derivation and numerical verification. The method by attaching an extra term to the lattice Boltzmann equation is still used, but the expression of the extra term is modified. It is the modified extra term that achieves the particularity of the new approach. This approach can not only introduce unsteady and non‐uniform body forces into momentum equations, but is also able to add an arbitrary source term to the continuity equation. Both the macroscopic equations from multi‐scale analysis and the simulated results of typical examples show that the accuracy with second‐order convergence can be guaranteed within incompressible limit. Copyright © 2007 John Wiley & Sons, Ltd.