Abstract
In this paper, we propose a combined finite volume - finite element scheme, for the resolution of a specific low-Mach model expressed in the velocity, pressure and temperature variables. The dynamic viscosity of the fluid is given by an explicit function of the temperature, leading to the presence of a so-called Joule term in the mass conservation equation. First, we prove a discrete maximum principle for the temperature. Second, the numerical fluxes defined for the finite volume computation of the temperature are efficiently derived from the discrete finite element velocity field obtained by the resolution of the momentum equation. Several numerical tests are presented to illustrate our theoretical results and to underline the efficiency of the scheme in term of convergence rates.
Highlights
Variable density and low Mach numbers flows have been widely investigated for the last decades
Based on a time splitting, this combined method allows to solve the mass conservation equation by a finite volume method, whereas the momentum equation associated with the divergence free constraint and the temperature one are solved by a finite element method
The finite volume scheme is classically obtained by integrating equation (3.3) on a control volume K, that is: mK
Summary
Variable density and low Mach numbers flows have been widely investigated for the last decades. The originality of the model considered here relies on the dynamic viscosity of the fluid being explicitly given as a function of the temperature, as introduced in [4] and generalized in [5] In this recent work, the authors establish the global existence of weak solutions in the three-dimensional case with no smallness assumption on the initial velocity. Based on a time splitting, this combined method allows to solve the mass conservation equation by a finite volume method, whereas the momentum equation associated with the divergence free constraint and the temperature one are solved by a finite element method It allows, in particular, to preserve the constant density states and to ensure the discrete maximum principle.
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