  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.
