Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER). (arXiv:2105.00048v1 [physics.flu-dyn]) Leave a comment

We show how a complete mathematical description of a complicated physical
phenomenon can be constructed from observational data via a hybrid approach
combining three simple and general ingredients: physical assumptions of
smoothness, locality, and symmetry, a weak formulation of differential
equations, and sparse regression. To illustrate this, we extract a complete
system of governing equations describing flows of incompressible Newtonian
fluids — the Navier-Stokes equation, the continuity equation, and the boundary
conditions — from numerical data describing a highly turbulent channel flow in
three dimensions. The hybrid approach is remarkably robust, yielding accurate
results for very high noise levels, and should thus work equally well for a
wide range of experimental data. In addition, this approach provides easily
interpretable information about the relative importance of different physical
effects (such as viscosity) as well as useful insight into the quality of the
data, making it a useful diagnostic tool.

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