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arXiv · 2007.08679

Versatile Mixed Methods for Non-Isothermal Incompressible Flows

Edward A. Miller·Xi Chen·David M. Williams
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Abstract

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.

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Edward A. Miller, Xi Chen, David M. Williams. 2020-07-16. Versatile Mixed Methods for Non-Isothermal Incompressible Flows. https://arxiv.org/abs/2007.08679

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