A velocity divergence constraint for large-eddy simulation of low-Mach flows

The velocity divergence (rate of fluid volumetric expansion) is a flow field quantity of fundamental importance in low-Mach flows. It directly affects the local mass density and therefore the local temperature through the equation of state. In this paper, starting from the conservative form of the sensible enthalpy transport equation, we derive a discrete divergence constraint for use in large-eddy simulation (LES) of low-Mach flows. The result accounts for numerical transport of mass and energy, which is difficult to eliminate in relatively coarse, engineering LES calculations when total variation diminishing (TVD) scalar transport schemes are employed. Without the correction terms derived here, unresolved (numerical) mixing of gas species with different heat capacities or molecular weights may lead to erroneous mixture temperatures and ultimately to an imbalance in the energy budget. The new formulation is implemented in a publicly available LES code called the Fire Dynamics Simulator (FDS). Accuracy of the flow solver for transport is demonstrated using the method of manufactured solutions. The conservation properties of the present scheme are demonstrated on two simple energy budget test cases, one involving a small fire in a compartment with natural ventilation and another involving mixing of two gases with different thermal properties.