The Effect of Discretization Error on Training of Machine-Learned Turbulence Models

A study on the effect of discretization error (DE) on Machine-Learning (ML) turbulence models is conducted. Data Assimilation and Field Inversion is used to learn turbulence models on three different grid resolutions for the simulation of hypersonic flow over a flat plate. Two kinds of training are conducted to learn a mapping between local scalar invariants and turbulent transport quantities. The first training uses a very fine grid as ``truth'' data, and the second uses velocity and temperature boundary layer profiles from a direct numerical simulation of hypersonic flow over a flat plate. It is found that ML turbulence models have enough degrees of freedom to correct for DE, but that physics-based ML turbulence models exhibit nonphysical results for untrained variables when a large amount of DE is present on training grids. It is also found that the relationship between DE during training and model error during testing is not 1:1 and that small amounts of DE during training can have disproportionate impacts on the final turbulence model.