Speaker
Description
Large-Eddy Simulation (LES) are state-of-the-art in engineering applications of Computational Fluid Dynamics (CFD). Fine grids offer high accuracy at high cost, whereas coarse grids require additional modeling assumptions that limit predictive capabilities. This dilemma is addressed by Extended LES (XLES). The original XLES formulation [1] utilized the One-Dimensional Turbulence (ODT) model [2] as a high-fidelity stochastic subgrid-scale (SGS) model that autonomously evolves instantaneous turbulent microscales in a dimensionally reduced setting.
For incompressible flow, XLES utilizes a coarse VLES grid of control volumes which solves the Poisson equation for the pressure to communicate large-scale information to the three auxiliary ODT grids carrying the SGS information. These grids have resolution N²_VLES*N_ODT$, where N_VLES and N_ODT denote the number of grid cells in the coarse VLES grid and a fully resolved 1-D ODT grid that is perpendicular to the VLES plane with resolution N²_VLES respectively, see [3]. The three ODT grids compose the 3-D Cartesian domain. The XLES model is more costly than any VLES, but less expensive than highly resolved LES, and naturally, than DNS, for which the spatial resolution requirements can be roughly estimated as N³_DNS ≅ N³_ODT. The XLES approach effectively removes the bottleneck of the Poisson solver, which operates on the coarse VLES grid with N³_VLES cells.
Building upon a recently developed C++ solver [4], the contribution to the conference will demonstrate and discuss relevant capabilities of XLES considering 3-D turbulent channel flow. The discussion will focus on the convergence properties of the XLES, evaluating how the LES resolution N_VLES affects the flow statistics disentangled from the stochastic SGS model.
References
[1] C. Glawe, H. Schmidt, A. R. Kerstein, and R. Klein. ”XLES Part I: Introduction to Extended Large Eddy Simulation.”, (2015) arXiv preprint arXiv:1506.04930.
[2] A. R. Kerstein. “One-Dimensional Turbulence: Model Formulation and Application to Homogeneous Turbulence, Shear Flows, and Buoyant Stratified Flows.” Journal of Fluid Mechanics 392 (1999): 277–334. https://doi.org/10.1017/S0022112099005376
[3] J. A. Medina Méndez, C. Glawe, T. Starick, M. S. Schöps, and H. Schmidt. ”IMEX-ODTLES: A Multi-Scale and Stochastic Approach for Highly Turbulent Flows.” Proceedings in Applied Mathematics and Mechanics 19 (2019): e201900433.
https://doi.org/10.1002/pamm.201900433
[4] P. Marinković, J. A. Medina, M. S. Schöps, M. Klein, and H. Schmidt. ”Experiences From the Bottom-Up Development of an Object-Oriented CFD Solver with Prospective Hybrid Turbulence Model Applications.” Proceedings in Applied Mathematics and Mechanics 25 (2025): e202400190. https://doi.org/10.1002/pamm.202400190
