A stress transport equation model for simulating turbulence at any mesh resolution

Prior work has demonstrated the effectiveness of using two-equation closures as the basis for universal, self-adapting turbulence models that are effective at any mesh resolution (Perot and Gadebusch in Phys. Fluids 19:115105, 2007). In order to demonstrate the broad applicability of the fundamental approach, the same behavior is now demonstrated for a second-moment closure (SMC). The SMC has the advantage over the earlier two-equation universal closure of being more accurate in the coarse mesh limit and of having a natural mechanism for backscattering energy from the modeled to the resolved turbulent fluctuations. The mathematical explanation for why Reynolds averaged (RANS) transport equation closures are applicable at any mesh resolution, including the large eddy simulation (LES) regime, is reviewed. It is demonstrated that for the problem of isotropic decaying turbulence, the SMC model produces good predictions at any mesh resolution and with arbitrary initial conditions. In addition, it is shown that the proposed model automatically adapts to the mesh resolution provided. The self-adaptive nature of the method is clearly observed when different initial conditions are used. It is shown that classic RANS models (often thought to produce steady and smooth solutions) can produce three-dimensional, unsteady, and chaotic solutions when generalized correctly and when provided with sufficient mesh resolution. The implications of these observations on the fundamental theories of RANS and LES turbulence modeling are discussed.