Constructing the body source for high-order lattice Boltzmann method

This paper presents a novel strategy for constructing body source terms in the high-order lattice Boltzmann method (LBM), designed to efficiently introduce various physical phenomena by modifying the non-equilibrium distribution function. The source term, expressed as a Hermite polynomial, provides a flexible framework for simulating complex fluid flows. Three typical source terms are given: a body force source for gravity-driven flows, a thermal dissipation source for controlling the Prandtl number, and a pressure tensor source for modeling multiphase flows. Chapman-Enskog analysis confirms that the source terms recover the expected macroscopic equations. Notably, the proposed strategy eliminates the need for explicit construction of the collision operator, a challenge in conventional approaches for handling diverse physical scenarios. Furthermore, the method is compatible with the traditional BGK model, ensuring its applicability to various high-order lattices. The model's accuracy and versatility are validated through a series of benchmark tests, showing excellent agreement with existing literature results.