Reynolds averaged Navier Stokes (RANS) models are the industry standard when it comes to computational fluid dynamics (CFD). RANS models have notable shortcomings as the
Reynolds stress is modelled locally and does not include temporal behaviour. Therefore,
current RANS models fail to make accurate predictions in areas of out-of-plane straining,
high streamline curvature and significant anisotropic Reynolds stresses.
Data augmented RANS models have shown promise to improve accuracy, with sparse regression and machine learning algorithms being able to train models between high fidelity
data and RANS. The current data driven models have problems, as they lack generalisability between data-sets, are difficult to interpret and only provide a local, non-temporal
correction or prediction for the Reynolds stresses.
The current work will explore sparse regression routines, in particular PDE FIND, for
the purpose of creating a non-local, temporal transport equation from data. Rather than
using high-fidelity turbulence data, a self-developed model problem, dubbed the ψ − ϕ
system, is created to replicate the uncertainties related to turbulence modelling. Multiple
candidate libraries for PDE FIND are tested, with the greatest emphasis on libraries
lacking a part of the true functional form, known as incomplete candidate libraries.
Incomplete candidate libraries are found to benefit from using highly correlated replacement functions for the missing function with an exception being a candidate library lacking
the correct production term. Even if models were trained poorly, PDE FIND was able to
identify the most important functions with an accurate coefficient.
PDE FIND could potentially create an universal transport equation to model the residual
between high fidelity data and RANS, but only if there are enough highly correlated
candidate functions and the production terms are well known or well represented in the
candidate library.