2020/07/16 by Miller, Edward A., Chen, Xi, Williams, David M.
#65M12 #65M60 #76D05 #76M10 #Computational Physics (physics.comp-ph) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2007.08679
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.