Case study · LES validation

LES VALIDATION FROM A SPHERE TO THE AHMED BODY

Before AOX LES runs on a car, it is checked against shapes with published answers: the drag on a sphere, then the pressure and wake behind the Ahmed body.

2026.10.02

Time-averaged speed on the symmetry plane of the Ahmed body with a 35° slant, from AOX LES, close in on the slant and the slow wake behind the base

Sphere drag difference from the reference solution at Re 100: 1.7%
Base + slant pressure drag on the Ahmed body (experiment 0.249): 0.250
Experimental pressure taps compared point by point: 457
Gap between two independent drag measurements: 0.010%

Benchmarks with published answers. Absolute drag on full cars is still being certified, so AOX reports differences between shapes as its most reliable result.

01 / WHY BENCHMARKS

Known answers first.

Before a solver is trusted on a car, it has to reproduce flows whose answers are already known. AOX LES is checked on two of them.

First a sphere, where the drag is known precisely. Then the Ahmed body, the standard validation shape of automotive aerodynamics.

02 / THE SPHERE

Within 1.7% of the reference.

At Reynolds number 100 the flow around a sphere is steady. Fornberg (1988) computed its drag coefficient directly: 1.0845. AOX LES gives 1.1030, 1.7% higher.

AOX LES drag coefficient, Re 100: 1.1030
Reference, Fornberg (1988) direct computation: 1.0845

Time-averaged streamwise velocity with streamlines on the mid-plane of a sphere at Reynolds number 100, from AOX LES, with a short region of slow, recirculating flow directly behind the sphere — Time-averaged streamwise velocity on the mid-plane around the sphere at Re 100, from AOX LES.

The box needs room.

Giving the flow more room ahead of the sphere brought the error down from +6.1% to +2.2%.

Two ways to measure drag.

The force on the wall and the momentum the air loses are independent measurements of drag. They agree within 0.010%.
Drag read over a stretch of the box with no body in it comes out at −0.000015, close to zero.

03 / THE AHMED BODY

457 pressure taps, point by point.

The Ahmed body (Ahmed, Ramm & Faltin, 1984) is a 1,044 mm long reference shape with a slanted rear. With a 35° slant, AOX LES is compared tap by tap with the ERCOFTAC Classic Collection experiment, case082 / AC1-05 (Lienhart, Stoots & Becker; surface pressures by Lienhart & Schenk).

Mean base pressure coefficient (experiment −0.220): −0.218
RMS difference across all 457 taps: 0.058

Pressure drag, region by region.

Integrating the surface pressure over the base and the slant gives their share of the drag.

Region	AOX LES	Experiment
Base	0.126	0.122
Slant	0.124	0.127
Base + slant	0.250	0.249

Pressure drag coefficient from surface pressure integrated over each region. Ahmed body, 35° slant.

Same body, two slants.

At 25° the flow follows the slant down to the base. At 35° it breaks away from the slant.

Time-averaged speed on the symmetry plane of the Ahmed body with a 25° slant, from AOX LES; fast air bends down along the slant towards the base — 25° slant: the flow follows the slant.

Time-averaged speed on the symmetry plane of the Ahmed body with a 35° slant, from AOX LES, on the same window and colour scale; fast air carries straight on past the slant, leaving a large slow region over the slant and the base — 35° slant: the flow breaks away.

04 / THE WAKE

Five slices behind the body.

Behind the 35° body, AOX LES velocity profiles are set against laser Doppler (LDA) measurements by Lienhart et al. at five stations: x = −88, 0, 80, 200 and 500 mm.

Five panels of streamwise velocity against height at x = −88, 0, 80, 200 and 500 mm behind the 35° Ahmed body, comparing AOX LES lines with measured points from Lienhart et al. — Streamwise velocity, 35° slant. Lines: AOX LES. Circles: Lienhart et al. LDA data from ERCOFTAC case082, replotted on our axes.

05 / MATCHING WALL FRICTION

Tuned to the flow, not the drag.

The grid cannot resolve the whole boundary layer, so AOX models the friction at the wall.

We tuned that wall model against the measured wake. On both the 25° and the 35° body, one setting gave the smallest error in the wake velocity.

Wake velocity-profile error across wall-model settings. Both slants are lowest at the same setting.

Why not tune for drag?

Drag alone would pick a different setting. Take away too much wall friction and a wrong flow field can still return the right drag. AOX uses the setting that gets the flow field right.

06 / REPEATABLE BY DESIGN

Same setup, same answer.

Identical results when the same setup is re-run, on two different servers: 17 digits
Result spread between GPU types, before and after our fix: 2.85% → 0.066%
Checks run before every validation run: 63
One standard Ahmed run, after moving to the production code path: 409 → 35 min

Every validation run is archived with its source bundle, then re-computed from the archive alone to confirm it reproduces.
Each of the seven measurement tools reports numbers only after it has been certified on a reference run.

07 / REFERENCES

References

Fornberg, B. (1988). Steady viscous flow past a sphere at high Reynolds numbers. J. Fluid Mech. 190.
Ahmed, S.R., Ramm, G. & Faltin, G. (1984). Some salient features of the time-averaged ground vehicle wake. SAE 840300.
Lienhart, H., Stoots, C. & Becker, S. (2003). Flow and turbulence structures in the wake of a simplified car model. SAE 2003-01-0656.
ERCOFTAC Classic Collection, case082 (AC1-05). Wake data by Lienhart, Stoots & Becker; surface pressures by Lienhart & Schenk.

CASE STUDIES

LES VALIDATION FROM A SPHERE TO THE AHMED BODY

Known answers first.