## Survey of Computational Method

A survey of the computational technique used to solve the Navier-Stokes equations is given in the following slides describing DFS as Direct Finite Element Simulation:

with some glimpses here:

- Airflow interacting with vocal chords
- Airflow around a car
- Bloodflow in heart
- Flow around mixer in exhaust system.

## Computation Can Now Replace Wind Tunnel

Wind tunnels have been used extensively in the development of flight in the 20th century, because the computational techniques have not been powerful enough.

But it is impossible to put an Airbus 380 into a wind tunnel and thus computing is the only possibility. Putting a toy model of an Airbus 380 into a wind tunnel is possible, but it is impossible to reliably upscale the results to the real size because of compressibility and boundary layer effects.

Computation is thus the only possibility of evaluating a new design which is not very similar to an old already tested one.

It is important to understand that it is now possible to accurately simulate the aerodynamics of a full airplane which opens entirely new possibilities of innovative design. The corresponding situation in the aerodynamics design of cars is addressed in Computing can replace wind tunnel.

A technology shift from wind tunnels to computational simulation is now to be expected.

## Slip and Rounded Trailing Edge

Navier-Stokes/slip computations for a long NACA0012 wing with 1% rounded trailing edge show good agreement with wind tunnel experiment over the whole range of angles of attack through stall, see NACA0012 and Wind Tunnel Experiments.

## Danger of No-Slip at Sharp Trailing Edge

Navier-Stokes/slip computation for a NACA0012 with a sharp trailing edge may give reasonable values of lift and drag for angles of attack well below stall, but gives seriously incorrect values for stall angles. The effect of a slip boundary condition at an edge is to effectively set the flow velocity to zero and thus act as an artificial un-physical mechanism for retardating the flow and thereby allow separation at the trailing edge without high pressure, and thereby give rise to a more or less reasonable flow field. The no-slip condition at a sharp trailing edge is a “fix” which can give reasonable values of lift and drag before stall, but the “fix” is unphysical and very dangerous because the critical moment of stall cannot be captured.

Realistic simulation requires resolution of the flow at a rounded trailing edge with a diameter of about 1% of the chord length, which is computationally feasible with less than a million mesh points.