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IMEX based multi‐scale time advancement in ODTLES
Author(s) -
Glawe Christoph,
Medina M. Juan A.,
Schmidt Heiko
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800098
Subject(s) - discretization , reynolds averaged navier–stokes equations , large eddy simulation , turbulence , reynolds number , mathematics , scale (ratio) , direct numerical simulation , bounded function , mathematical optimization , statistical physics , computer science , algorithm , physics , mathematical analysis , mechanics , quantum mechanics
Abstract 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 (2015). This scheme can be stabilized by reducing the CFL number for the explicitly discretized LES terms down 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 (2015) limited the overlap consistently to one LES cell and used a stable Runge Kutta (RK) discretization, maintaining, however 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. For the problems investigated, the results indicate a performance increase of the IMEX scheme by a factor of 17 based on the ratio of applied CFL numbers. This allowed simulations of a turbulent channel flow with characteristic friction Reynolds number R e τ = 2040 on one Banana Pi single board computer. We compare results to available DNS data and discuss in general the efficiency and potential of ODTLES for high Reynolds number flows.