A study on the inclusion of body forces in the lattice Boltzmann BGK equation to recover steady-state hydrodynamics

► We derive a body force model expression in the lattice Boltzmann (LB) method. ► This model recovers exactly the steady incompressible Navier-Stokes equations. ► The analysis is performed theoretically (Chapman-Enskog analysis) and numerically. ► The correct form of the LB body force model differs from the time-dependent case. ► The model yields the most accurate results for varying body forces in steady flows.