Residual-based variational multiscale methods for laminar, transitional and turbulent variable-density flow at low Mach number

In the present study, residual-based variational multiscale methods are developed for and applied to variable-density flow at low Mach number. In particular, two different formulations are considered in this study: a standard stabilized formulation featuring SUPG/PSG/grad-div terms and a complete residual-based variational multiscale formulation additionally containing cross- and Reynolds-stress terms as well as subgrid-scale velocity terms in the energy-conservation equation. The proposed methods are tested for various laminar flow test cases as well as a test case at laminar via transitional to turbulent flow stages. Stable and accurate results are obtained for all numerical examples. Substantial differences in the results between the two approaches do not become notable until a high temperature gradient is applied and the flow reaches a turbulent flow stage. The more pronounced influence of adding subgrid-scale velocity terms to the energy-conservation equation on the results than adding analogous terms to the momentum-conservation equation in this situation appears particularly noteworthy.