fredag 22 juli 2022

Computability of Turbulent vs Laminar Flow

Euler Computational Fluid Dynamics CFD shows that mean values such as lift and drag from the turbulent flow around all sorts of vehicles/bodies moving through air or water are computable at low computational cost, while point values of the fluid flow and body forces in space and time are uncomputable. Euler CFD shows that the mean values are stable quantities insensitive to mesh resolution and small changes of geometry, while point values are very sensitive. 

In Euler CFD this is captured by a dual linearised solution, which in the case of an underlying turbulent oscillating base flow through cancellation can be of moderate size as an expression of mean value stability. This comes out as independence of lift and drag for flow with large Reynolds number beyond drag crisis.  

Laminar flow on the other hand may be less stable because of base flow without oscillation and cancellation, and thus may require large computational cost to correctly capture. It comes out as a possible dependence of lift and drag on smaller Reynolds numbers before drag crisis. An example of laminar flow is potential flow which is unstable/unphysical and thus uncomputable as solution of the Euler equations.

So, in certain (mean value) sense, turbulent flow can be more easy to compute/predict than laminar flow, which can be viewed to be paradoxical, but then in fact is not. 


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