A combined finite volume - finite element scheme for a low-Mach system involving a Joule term

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.