On a certified Smagorinsky reduced basis turbulence model

TL;DR

This paper introduces a reduced basis Smagorinsky turbulence model for steady flows, employing empirical interpolation and a posteriori error estimation to significantly accelerate computations.

Contribution

It develops a novel reduced basis approach with certified error bounds for the Smagorinsky turbulence model, enhancing computational efficiency and reliability.

Findings

Achieved over 1000x speedup in 2D flow benchmarks

Implemented the model in FreeFem++ for numerical validation

Extended a posteriori error estimation to non-linear eddy diffusion

Abstract

In this work we present a reduced basis Smagorinsky turbulence model for steady flows. We approximate the non-linear eddy diffusion term using the Empirical Interpolation Method, and the velocity-pressure unknowns by an independent reduced-basis procedure. This model is based upon an a posteriori error estimation for Smagorinsky turbulence model. The theoretical development of the a posteriori error estimation is based on previous works, according to the Brezzi-Rappaz-Raviart stability theory, and adapted for the non-linear eddy diffusion term. We present some numerical tests, programmed in FreeFem++, in which we show an speedup on the computation by factor larger than 1000 in benchmark 2D flows.