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Gradient Numerics
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Computed cases

Twenty-two figures, five geometries.

Solver output as it came out, with its color bar. Tap a thumbnail to change the view.

  1. Submarine reference hull06
  2. Box-wing UAV06
  3. Fixed-wing UAV, wall shear stress04
  4. Finned slender body03
  5. Velocity field with shock waves03

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01p · viridis · −4.0 … 4.0

Submarine reference hull

Six views of the same simulation, on the same color scale.

Geometry
DARPA SUBOFF, hull with sail and rudders
Field
static pressure p
Color scale
viridis
Range
−4.0 … 4.0
Solver
OpenFOAM 13, post-processing in ParaView
Submarine hull in three-quarter view from above, pressure field on a viridis scale, peak at the bow.
three-quarter view from above

02p · rainbow · −150 … 150

Box-wing UAV

How the load shifts between the two wings.

Geometry
box-wing UAV, engine in the fuselage
Field
static pressure p
Color scale
rainbow
Range
−1.5e+02 … 1.5e+02
Box-wing UAV in three-quarter view from above, surface pressure field: blue at the tips, red on the leading edges.
three-quarter view from above

03wallShearStress · rainbow · 0 … 3.0

Fixed-wing UAV, wall shear stress

Where the boundary layer is still attached, and where it is about to separate.

Geometry
fixed-wing UAV, fixed landing gear, tractor propeller
Field
magnitude of wallShearStress
Color scale
rainbow
Range
0.0 … 3.0
Solver
OpenFOAM 13
Fixed-wing UAV with landing gear in three-quarter view, wall shear stress magnitude on the surface: red on the leading edges, blue on the upper surfaces.
three-quarter view

04Cp · rainbow · −0.3 … 0.3

Finned slender body

The pressure coefficient is dimensionless, so one scale works across speeds.

Geometry
slender body of revolution, four fins
Field
pressure coefficient Cp
Color scale
rainbow
Range
−3.0e−01 … 3.0e−01
Long slender body with four tail fins, seen at an angle and colored by pressure coefficient.
three-quarter view

05Velocity Magnitude · 0 … 489 m/s

Velocity field with shock waves

At 489 m/s, the flow can no longer be treated as incompressible.

Geometry
finned slender body
Field
velocity magnitude [m/s]
Color scale
rainbow
Range
0.0 … 4.89e+02
Solver
Ansys 2026 R1
Velocity contour plane around a slender body: a blue wake and oblique shock waves leaving the nose, on an orange background.
contour plane