## måndag 16 december 2019

### Prescription vs Prediction in CFD

Recent posts compare the standard methods of CFD based on turbulence and wall models (RANS, LES and DES as a combination), with DFS Direct Finite Element Simulation without turbulence and wall models as best possible solution of Euler's equations.

DFS has shown to accurately predict complex aerodynamics such as the stall of an airplane by capturing both turbulence and flow separation from first principle physics. DFS thus predicts the full flight characteristics of an airplane with the only input being the shape of the airplane. DFS not only predicts flow separation but also makes it understandable as 3d rotational slip separation with point or line stagnation.

This is a stunning example of the ideal according to Einstein of a mathematical model capable of predicting true physics without input of physical parameters. It is like predicting the circumference of a circle with radius 1 to be $2\pi$, just much more complicated and surprising.

With the standard methods of RANS-LES prediction is replaced by prescription mediated through the turbulence and wall models containing many parameters.  As a result RANS-LES cannot truly predict flow separation since that has to be built into the wall model, by either prescribing the flow to stay attached to a smooth solid wall and separate at a corner, or separate under influence of an "adverse pressure gradient".

The main novelty of DFS is thus the possibility of true prediction, which is not possible with RANS-LES which include prescription.  This connects to Bohr's comment to Einstein's claim that God does not trow dice, in the form:
• Einstein, stop telling God what to do!
RANS-LES tells physics what to do. DFS predicts what physics does.

 DFS prediction of stall of a jumbojet with flow separation on top of the inner part of the wing, in close agreement with observation.