IMEX based multi‐scale time advancement in ODTLES

In this paper we overcome a key problem in an otherwise highly potential approach to study turbulent flows, ODTLES (One-Dimensional Turbulence Large Eddy Simulation). From a methodological point of view, ODTLES is an approach in between Direct Numerical Simulations (DNS) and averaged/filtered approaches like RANS (Reynolds Averaged Navier-Stokes) or LES (Large Eddy Simulations). In ODTLES, a set of 1D ODT models is embedded in a coarse grained 3D LES. On the ODT scale, the turbulent advection is modeled as a sequence of stochastic eddy events, also known as triplet maps, while the other (deterministic) terms are fully resolved in space (along the ODT- line) and time. Schmidt et al. first (2008) introduced ODTLES and Gonzalez et al. (2011) applied the model for a variety of wall-bounded flow problems. Although the results were notable for a first proof of concept, the numerical methods used are subject to debate. First of all, an unstable discretization for the large scale 3D advective terms was used as shown by Glawe (2013). The scheme can be stabilized by reducing the CFL number for the explicitly discretized LES terms to the order of the small scale ODT time step, but this of course reduces the advantage of the ODTLES multi-scale approach. The stochastic ODT eddies were also allowed to overlap two LES cells introducing an artificial smoothing (stabilizing) effect. Glawe (2013) limited the overlap consistently to one LES cell and used a stable Runge Kutta (RK) discretization, however maintaining the low CFL number problem. In this paper we adapt a new implicit/explicit (IMEX) time scheme to ODTLES in order to remedy the small CFL number issue.