Boundary layer mesh generation
The scope here is to generate a quasistructured mesh from a complex geometry. This
is require to solve accurately the NavierStokes equations. The approach developed here is based
on local mesh modification operators. Key elements
 Robustness to geometry complexity
 CPU time to generate the boundary layer mesh (all examples are generated in less that 5 min on a laptop)
 Ability to mix quasistructured mesh and anisotropic mesh adaptation
 Ability to generate hybrid elements
A complex scud geometry

Boundary layer mesh

Boundary layer mesh

Boundary layer mesh

Landinggear geometry

Boundary layer mesh

Boudary Layer mesh

Boundary layer mesh

Anisotropic m6 wing

Boundary layer mesh

Boundary layer mesh

Boundary layer mesh

Shuttle geometry

Boundary layer mesh

Boundary layer mesh

Boundary layer mesh

Hightlift geometry

Boundary layer mesh

Boundary layer mesh

Boundary layer mesh

Fullscale sonic boom simulation
We consider in this example the accurate prediction of the pressure signal
below the SSBJ design provided by DassaultAviation. The length of the aircraft is L=43 m
while the distance of observation from the aircraft is denoted by R.
The aircraft is put in a 10 km domain.
The initial mesh was generated automatically by using an advancingfront technique.
The size ratio in the initial mesh is h_min/h_max = 1e^9 and the volume
of the elements ranges from 5.4e^11 to 4.7e^10.
The flow condition is Mach number 1.6 with an angle of attack of 3 degrees.
Our intent is to observed the pressure field for various R up to 9 km.
This corresponds to a ratio R/L of about 243. According to the flow conditions,
for R = 9 km, the length of the propagation of the shock waves emitted by the SSBJ is actually around 15 km.
Computational Domain

Aircraft geeomtry

Adaptated surface mesh

Cut in the volume mesh

Cut in the volume mesh

Closer view near the aircraft

Upper view of the mesh

Anisotropic mesh at 4km

Anisotropic mesh at 9km

Pressure signal at 1km

Pressure signal at 5km

Pressure signal at 9km

Supersonic shock/Boundary layer interaction
We study a supersonic shock/boundary layer interaction.
The test case is depicted in the first Figure.
The shock waves are generated by a double wedge wing at Mach 1.4 with an
angle attack of 0 degree and a
Reynolds number of 3.4 10^6. Only the plate is treated as a viscous body.
The final mesh is composed of 280 000 vertices and 1.3 millions tetrahedra and is obtained after 20 iterations.
In this example, we control
the interpolation error on the Mach number.
The unstructured boundary layer mesh height is around 10^7 near the plate.
Computational domain

Initial computational mesh

Final adapted mesh

Mach isovalues

Mesh near the shock

Mach isovalues

Velocity stream

Anisotropic mesh (2nd shock)

Mach isovalues (2nd shock)

Velocity stream (2nd shock)

Highfidelity capturing of wingtip vortices with adjoint methods
In this example, we study the accurate prediction of wing tip vortices at large distance in the wake
for transsonic flow conditions.
The jet is flying at transonic cruise speed with Mach number 0.8 and an angle of attack of 3 degrees.
The computational domain is a cylinder of radius 250 m and of length 700 m.
The adjointbased
adaptation is based on the vorticity functional.
The complexity of this simulation is inherited from the specificity
of wing tip vortices.
As the aircraft is flying at a transonic speed,
the flows is composed of both shocks and smooth vortices.
These phenomena have different magnitudes and mathematical properties.
Across a shock, most variables become discontinuous whereas a
vortex corresponds to a smooth variation of the variables
while having a very small amplitude.
An extraction of the pressure across the wing extrados where a shock occurs (green curve)
is superposed to the pressure variation in the wake across a vortex located $400$ m behind the aircraft (red curve).
The amplitude of the vortex is less than 2\% of the amplitude of the shock.
Moreover, the smoothness property of the vortex is a supplementary difficulty.
Detecting and preserving these vortices are still a challenge in the field of CFD.
Falcon geometry

Comparison between shock and vortex

Pressure isosurface

Pressure isosurface

Pressure 100m behin the aircraft

Pressure isovalues at 100 m

Pressure isolines

Pressure at 200 m

Isovalues

Pressure isolines at 200 m

Pressure at 400m

Pressure isovalues at 400 m

Pressure isolines at 400 m

Anisotropic mesh

Anisotropic mesh

Anisotropic mesh

Unsteady mesh adaptation
From a mesh generation standpoint, anisotropic unsteady mesh adaptation
is still an unachieved goal.
Many difficulties are added in comparison
with steady simulations or even isotropic unsteady adaptation as hrefinement.
Consequently, the full gain, both in cpu time and accuracy, that may be expected
when anisotropic features are present in the flow field
is barely obtained. At first,
the surface mesh adaptation becomes critical as successive
refinements and unrefinements may occur along the simulation.
In the meantime, it is also mandatory to maintain a good approximation of the geometry.
Then, the flow solver time step depends on the quality of the volume mesh. Consequently the cpu time
of the whole simulation linearly depends on the element having the worse quality.
One error in the mesh generation process can lead to a cpu time multiplied by 100 so that
the gain of the anisotropic approach is completely lost.
We two examples of unsteady simulation, a shock wave impacting a wedge geometry and
a blast propagation around the capitol geometry.
Initial 2state solution

Anisotropic mesh

Density isovalues

Cut in the mesh

Density isovalues

Capitol geometry

Anisotropic surface mesh

F15 equipped with a Quiet Spike©
We consider in this example the accurate prediction
of the midfield pressure signature of the F15 fighter equipped
with the Quiet Spike concept
during a supersonic flight. The aircraft is flying at Mach 1.8 with an angle of attack of 0 degree.
This concept was devised
to soften the sonic boom by splitting the initial strong bow shock
in several shocks of smaller amplitudes.
The Quiet Spike is composed of three cones linked by cylinders of increasing radius .
The smallest cylinder has a radius of 5 cm while the greatest one has a radius of 20 cm.
These sizes must be compared to the aircraft length 19.3 m and wingspan 13 m.
The scale variations of the geometry
give a first idea of the complexity of this simulation.
In the literature, this simulation is currently envisaged in a 2stage process by coupling a structured solver with an unstructured one.
This approach gives an accurate pressure field far below the aircraft with a limit at 70 m.
The adaptation is performed in L2 norm on the Mach number.
The final adapted meshes is composed of
10 050 445 vertices and 60 280 606 tetrahedra.
The final mesh automatically provides
an accurate signature 120 m below the aircraft while using only unstructured meshes.
Picture of f15 with Quiet Spike

Capturing of the back vortices

Mach isovalues

Mach isovalues with the mesh

Mach isovalues on the skin

Pressure distribution

Pressure signature R/L=1

Pressure at R/L=6

Mach isovalues near the spike

Mach isovalues near the spike
