  The purpose of this paper is to extend the versatile mixed methods originally
developed by Chen and Williams for isothermal flows in "Versatile Mixed Methods
for the Incompressible Navier-Stokes Equations," Computers & Mathematics with
Applications, 2020, (under review), to simulate non-isothermal incompressible
flows. These new mixed methods are particularly interesting, as with only minor
modifications they can be applied to a much broader range of flows, including
non-isothermal weakly-compressible flows, and fully-compressible flows. In the
main body of this paper, we carefully develop these mixed methods for solving
the Boussinesq model equations. Thereafter, we prove the L2-stability of the
discrete temperature field, and assess the practical behavior of the methods by
applying them to a set of well-known convection problems.
