“…The term involving is the body force term in the momentum equation due to buoyancy based on the low Mach number Boussinesq approximation, , where T is the fluid temperature [18]. The local equilibrium, , for each velocity direction is based on a local Mach number expansion of the Maxwell-Boltzmann distribution up to second order in the fluid velocity, , and is given by the following equation, (8) where wi are weights associated with the lattice and the macroscopic values of density, , and velocity, , are obtained from the following equations (9) The fluid kinematic viscosity, , is fixed based on the collision relaxation time, , the lattice space, , and the time step, t, and is given as (10) Equations (9) are moments of the distribution function and as is common in kinetic theories, it is possible to obtain higher order moments to include the thermal aspects of the fluid flow. However, thermal fluctuations in reality require many more particle velocities and the D3Q19 would therefore be insufficient.…”