Low-dissipation finite element strategy for low Mach number reacting flows

Abstract

The present paper extends the conservative finite element convective scheme proposed by Charnyi et al.(Journal of Computational Physics 337, 2017, 289–308) originally formulated for incompressible flows to the low Mach regime. Similar to Lehmkuhl et al.(Journal of Computational Physics 390, 2019, 51–65) stabilisation is only introduced for the continuity equation by means of a non-incremental fractional-step method, modified in order to account for variable density flows. The final scheme preserves momentum and angular momentum for variable density flows. The error of kinetic energy conservation is of order O(δthk+1), thus dissipation is limited. Standard stabilised finite elements are used for the scalars. Time integration is carried out by means of an explicit third order Runge-Kutta scheme for all equations. The proposed strategy is tested on a set of relevant cases with available reference data using large-eddy simulations. First, an anisothermal turbulent channel flow is assessed. Later, a technically premixed turbulent flame in a swirl-stabilized configuration is considered. And finally, a turbulent jet diffusion flame in a low-velocity co-flow has been studied. In all cases the performance of the presented low Mach formulation is fairly good, showing better accuracy than skew-symmetric like strategies.