# Computation Can Now Replace Wind Tunnel

· fluid mechanics
Authors

The milestone of computing the drag of car by solving the Navier-Stokes equations was passed in 2011 with the work reported in Adaptive Simulation of Turbulent Flow Past a Full Car Model, by N. Jansson, J. Hoffman and M. Nazarov: With about 10 million mesh points a C_D of 0.38 was computed, to be compared with measured 0.36.

A crucial feature of the computation is the use of a slip boundary condition as a model of small skin friction instead of the dictate by Prandtl to use no-slip causing thin boundary layers demanding quadrillions of mesh points thus making computational simulation of slightly viscous turbulent flow impossible. With slip it is possible and a wealth of applications are ready for computational harvest, see for example The Secret of Flight.

Wind tunnels for testing cars can now be dismantled and replaced by adaptive computation with major reductions in cost and lead time. Some snapshots from the article:

## Mesh Refinement and Flow Velocity

1. ### Anders Logg

Impressive simulation! But what happens beyond 1e7? The plot of the drag coefficient does not seem to indicate any kind of convergence and seems to stop by chance at the correct value. Maybe there are more data points missing in the plot?

2. ### claesjohnson

Ask the authors. But the C_D coeff is a mean-value over the force over all of the surface and over very long time and to give C_D with three decimals cannot be meaningful. To ask for an error below say 5% in either measurement or computation may be unreasonable.

3. ### Anders Logg

I agree, but the plot seems to indicate convergence towards something like 0.2 (???) which gives an error of 50%. But there may be more data points to support a value of 0.4.

4. ### claesjohnson

The difficulty is to get a value which is not too big since the model is more diffusive than reality modulo a very small contribution from skin friction. It is thus inceivable that computation would give 0.2. Or turned the other way, if it did somethIng would be wrong with the measurements.

5. ### Anders Logg

Does the skin friction parameter (beta) need to be adjusted to get agreement with experiments on a case-by-case basis, or is it a material parameter based on the paint used by Volvo?

6. ### claesjohnson

It is put to zero = full slip. The drag of different colors seem to be the same, according to measurements by Volvo (secret). The idea that a red car is faster seems to be an illusion.

7. ### Anders Logg

Nice that beta = 0 works so well! (But the convergence is still not convincing.)

8. ### claesjohnson

One can always ask for more, and it will come.

ok