COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Abstract
We present a novel approach to define the filter and relax steps in the evolve-filter-relax (EFR)
framework for simulating turbulent flows. The EFR main advantages are its ease of implementation and
computational efficiency. However, as it only contains two parameters (one for the filter step and one
for the relax step) its flexibility is rather limited. In this work, we propose a data-driven approach in
which the optimal filter is found based on DNS data in the frequency domain. The optimization step is
computationally efficient and only involves one-dimensional least-squares problems for each wavenumber.
Across both decaying turbulence and Kolmogorov flow, our learned filter decisively outperforms the
standard differential filter and the Smagorinsky model, yielding significantly improved accuracy in energy
spectra and in the temporal evolution of both energy and enstrophy. In addition, the relax parameter is
determined by requiring energy and/or enstrophy conservation, which enforces stability of the method and
reduces the appearance of numerical wiggles, especially when the filter is built in scarce data regimes.
Applying the learned filter is also more computationally efficient compared to traditional differential filters,
as it circumvents solving a linear system.
