SOLVING… LOADING FIELD
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LATTICE BOLTZMANN · D3Q19
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AERODYNAMICS

WORK IN PROGRESS

Wind tunnel

Z4 M COUPÉ · E8670 MPHHEADING 058°

VELOCITY MAGNITUDE · M/S

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FREE STREAM 31 M/S

SHOW
VIEW

DRAG TO TURN · SCROLL TO ZOOM · TRACERS RELEASED EVERY 200 MS OF FLOW TIME, TRAVELLING AT THE LOCAL SPEED

Results

SLIPSTREAM, 10 OCT 2026 · TIME-AVERAGED OVER THE LAST 7,000 STEPS · WORK IN PROGRESS

WORK IN PROGRESSThis is a home-built wind tunnel and its data is still being worked on. The solver is new, the model is a downloaded one with parts the real car does not have, the tunnel is far narrower than a real facility and the boundary layer is not resolved. Treat the figures as a record of where the work has got to, not as measurements of the car, and expect them to change as the solver and the model are corrected.

Through the body

SIDE-VIEW SECTIONS AT SIX DISTANCES FROM THE CENTRELINE · REV B SOLVE

SHOW
0.00 M FROM CENTRECentrelineThe car's own midline: the stagnation at the nose, the air accelerating over the screen and roof, and the dead air filling the wake behind the tail.
Side-view section through the car, centreline, coloured by air speedAIR →
0.30 M FROM CENTREInboardA third of the way out: the engine bay behind the kidneys, and the floor running under the car.
Side-view section through the car, inboard, coloured by air speedAIR →
0.60 M FROM CENTRESill lineOut near the sills, where the body is at its widest under the doors.
Side-view section through the car, sill line, coloured by air speedAIR →
0.75 M FROM CENTREWheel centresThrough the middle of each wheel. Cells at the tyre contact patches read unphysically and should be ignored.
Side-view section through the car, wheel centres, coloured by air speedAIR →
0.90 M FROM CENTREFlankSkimming the outside of the body at the shoulder, where the air is pushed aside by the wheel arches.
Side-view section through the car, flank, coloured by air speedAIR →
1.05 M FROM CENTREOutboardIn the air beside the car, just beyond the body.
Side-view section through the car, outboard, coloured by air speedAIR →

AIR SPEED: DARK VIOLET IS STALLED AIR, TEAL AND GREEN FREE STREAM (31 M/S), YELLOW ACCELERATED PAST IT · THE SCALE RUNS 0–50 M/S · THE BODY IS SHOWN SOLID, THE CABIN INCLUDED

Reading the picture

WHAT THE FIELD DOES AROUND THIS SHAPE · FROM THE REV B SOLVE

    How it was computed

    METHOD, AND WHERE IT STOPS BEING TRUE

    The results above are from the key Slipstream solve (10 October, stock model, 20 mm cells). The flow lines, the pressure skin and the notes under “Reading the picture” are from the earlier rev B solve at 30 mm, which also modelled open ducts and turning tyres; Slipstream does not yet, so those two sections below describe rev B.

    The solver

    This is a lattice-Boltzmann solve, the method most of the road-car industry now uses for exterior aero. Rather than solving the Navier–Stokes equations directly, it tracks packets of air moving between the cells of a fixed grid and colliding — and the correct fluid behaviour falls out of the bookkeeping. It handles messy geometry well, which matters here, because the geometry is the car.

    The model from the garage page was voxelised: every triangle rasterised onto a grid (20 mm in the Slipstream solves, 30 mm in rev B), the shell closed, and everything the outside air could not reach marked as solid. Air enters at the nose end of the domain at a fixed speed, leaves freely at the tail end, and the floor runs backwards at the same speed as the air — a rolling road, as a real tunnel would use.

    Air through the car, not just round it (rev B)

    The donor model has its grilles painted on rather than cut out, so the openings were authored to the real car's layout and carved out of the voxel body: the two kidneys, the lower intake and a corner duct each side. On the page the bodywork itself is left whole — cutting the same boxes out of the display mesh tore the grille surround — so the lines that vanish into the nose are going in where the real openings are. They feed a shrouded plenum, so the air cannot simply slip round the edge of the core, then pass through a radiator modelled as a porous slab — partial bounce-back, with the resistance set from a duct calibration to behave like a real core and condenser stack. Behind that is a firewall, so nothing vents into the cabin, and the only way out is a 30 mm slot across the trailing edge of the bonnet. That is a vent slot, deliberately, not the factory panel gap; a 5 mm shutline is far below anything this grid could resolve.

    Tyres that turn (rev B)

    The wheels do not rotate as geometry — they do not need to. In lattice Boltzmann the bounce-back off a solid cell can carry a wall velocity, so every cell on each tyre is given its own surface velocity from ω × r about the axle, at the speed that rolls without slip on the moving floor. The air leaves the surface with the right tangential momentum, which is how production solves treat a tyre. Checked first on a spinning cylinder: the air one cell off the surface comes out at 0.85 of the surface speed.

    Where tyre meets road is the awkward part. A circular section touching a moving floor is a singular corner and, left alone, squirts a spurious jet sideways. Each tyre is therefore cut to a flat 150 mm contact patch with vertical sides, which is both the standard fix and closer to what a loaded tyre actually does.

    Turbulence

    Nothing resolves every eddy on a car at road speed; that would need more grid than exists in this room. The small scales are handled by a Smagorinsky sub-grid model, which adds extra viscosity exactly where the strain rate is high. The large structures — the separation off the tail, the pair of trailing vortices, the wake's length — are resolved, and those are what set drag.

    Where it stops being true

    The grid is still coarse. In the Slipstream solves one cell is 20 mm and the car is 206 cells long; in rev B it was 30 mm and 138, with the gap under the floor three to four cells and each wheel 22 across. That is enough for the shapes of things and not enough for a boundary layer, so surface friction drag is understated while the staircase surface catches pressure a smooth panel would not.

    The radiator's resistance is tuned, not measured — no one has put a pressure drop across this car's core. The engine bay is empty behind the core, where a real one is full of engine, and the only outlet is the bonnet vent, where a real car dumps most of its cooling air under the floor.

    The donor model carries a splitter, side skirts and aftermarket wheels the real car does not, and the tunnel is narrow enough (10% blockage in the Slipstream solves, 19% in rev B) that the walls are closer to the car than any real facility would allow.

    The Reynolds number of the solve is far below the road value. For a bluff body whose separation points are set by sharp edges — the trailing edge of the hatch, the arch lips — the wake's shape is largely insensitive to that, which is why the picture is worth looking at. The absolute numbers are not.

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