A Critical Review of Forcing Schemes in Lattice Boltzmann Method: 1993–2019

Abstract

Lattice Boltzmann method (LBM) has emerged as an alternative method for the conventional computational fluid dynamics (CFD). LBM has a few advantages over traditional CFD, namely easy to apply, thermodynamics can be naturally integrated into the transport equations, etc. The complex physics is added to the governing equations via source terms. Nevertheless, there are many issues related to the method that needs to be carefully investigated and evaluated. One of these issues is implementing the force term. Since there are a few methods in implementing the force term in the open literature, the topic needs to review and assess in helping the readers and researchers in selecting the appropriate method. The present work focuses on the issue of implementing the momentum forces into the LBM. The work reviews, summarizes, and evaluates the published forcing schemes. The advantages, disadvantages, and constraints of each of them are presented. The literature review shows that there are about twelve forcing schemes proposed in the open literature. To the authors’ knowledge, there is no review published to compare and assess those schemes. The schemes can be classified according to implementing method into the LBM governing equation, namely implementing through the equilibrium distribution function, as a source term, and implementing through both equilibrium distribution function and source term. Also, the schemes can be grouped into four groups based on the form of the discrete lattice force term. Natural convection in a heated cavity is used as a platform for testing and comparing the reviewed schemes. The force term in the natural convection problem varies through the domain of integration, which is a function of the temperature. In other words, the force term is variable. The evaluated results show that all reviewed schemes yielded similar results and consistent with the benchmark solution. That refutes the claim of some authors that their scheme is more accurate than the others. We should mention that our conclusion is valid for single-phase flows. We are in the process of testing those schemes for multi-phase flows.