Large-Small Eddy Simulations: A Multi-Fidelity Method to Study Turbulence at Extreme Reynolds Numbers

We describe a recently proposed multi-fidelity method, which couples a lower fidelity large eddy simulation (LES) with an embedded high-fidelity, fully resolved small eddy simulation (SES) of a sub-region of interest. Such coupling is achieved by extracting a large-scale flow structure from an LES through filtering and subsequently injecting spatio-temporally interpolated data into the SES. The resulting “Large/Small Eddy Simulation” (L/SES) method is agnostic of the details of the system geometry, free from assumptions of equilibrium, homogeneity and isotropy, and is applicable to any realistically complex flow, both incompressible and compressible. The accuracy of the method is assessed for homogeneous isotropic turbulence using both a priori and a posteriori analysis for a wide range of Taylor-scale Reynolds numbers Re_λ > 600. We show that L/SES can achieve accuracy comparable to a DNS, with orders of magnitude reduction in computational cost. Implementation of this approach on the leadership-class exascale platforms holds promise to enable first-principles exploration of turbulent flows at extreme-Reynolds numbers representative of realistic flows both on Earth and in astrophysical systems.