Boundary layer mesh generation

The scope here is to generate a quasi-structured mesh from a complex geometry. This is require to solve accurately the Navier-Stokes equations. The approach developed here is based on local mesh modification operators. Key elements
A complex scud geometry
A complex scud geometry
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Landing-gear geometry
Landing-gear geometry
Boundary layer mesh
Boundary layer mesh
Boudary Layer mesh
Boudary Layer mesh
Boundary layer mesh
Boundary layer mesh
Anisotropic m6 wing
Anisotropic m6 wing
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Shuttle geometry
Shuttle geometry
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Hight-lift geometry
Hight-lift geometry
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh
Boundary layer mesh

Full-scale sonic boom simulation

We consider in this example the accurate prediction of the pressure signal below the SSBJ design provided by Dassault-Aviation. 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 advancing-front 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
Computational Domain
Aircraft geeomtry
Aircraft geeomtry
Adaptated surface mesh
Adaptated surface mesh
Cut in the volume mesh
Cut in the volume mesh
Cut in the volume mesh
Cut in the volume mesh
Closer view near the aircraft
Closer view near the aircraft
Upper view of the mesh
Upper view of the mesh
Anisotropic mesh at 4km
Anisotropic mesh at 4km
Anisotropic mesh at 9km
Anisotropic mesh at 9km
Pressure signal at 1km
Pressure signal at 1km
Pressure signal at 5km
Pressure signal at 5km
Pressure signal at 9km
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
Computational domain
Initial computational mesh
Initial computational mesh
Final adapted mesh
Final adapted mesh
Mach iso-values
Mach iso-values
Mesh near the shock
Mesh near the shock
Mach iso-values
Mach iso-values
Velocity stream
Velocity stream
Anisotropic mesh (2nd shock)
Anisotropic mesh (2nd shock)
Mach iso-values (2nd shock)
Mach iso-values (2nd shock)
Velocity stream (2nd shock)
Velocity stream (2nd shock)

High-fidelity capturing of wing-tip 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 adjoint-based 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
Falcon geometry
Comparison between shock and vortex
Comparison between shock and vortex
Pressure iso-surface
Pressure iso-surface
Pressure iso-surface
Pressure iso-surface
Pressure 100m behin the aircraft
Pressure 100m behin the aircraft
Pressure iso-values at 100 m
Pressure iso-values at 100 m
Pressure iso-lines
Pressure iso-lines
Pressure at 200 m
Pressure at 200 m
Iso-values
Iso-values
Pressure iso-lines at 200 m
Pressure iso-lines at 200 m
Pressure at 400m
Pressure at 400m
Pressure iso-values at 400 m
Pressure iso-values at 400 m
Pressure iso-lines at 400 m
Pressure iso-lines at 400 m
Anisotropic mesh
Anisotropic mesh
Anisotropic mesh
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 h-refinement. 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 2-state solution
Initial 2-state solution
Anisotropic mesh
Anisotropic mesh
Density iso-values
Density iso-values
Cut in the mesh
Cut in the mesh
Density iso-values
Density iso-values
Capitol geometry
Capitol geometry
Anisotropic surface mesh
Anisotropic surface mesh

F15 equipped with a Quiet Spike©

We consider in this example the accurate prediction of the mid-field 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 wing-span 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 2-stage 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
Picture of f15 with Quiet Spike
Capturing of the back vortices
Capturing of the back vortices
Mach iso-values
Mach iso-values
Mach iso-values with the mesh
Mach iso-values with the mesh
Mach iso-values on the skin
Mach iso-values on the skin
Pressure distribution
Pressure distribution
Pressure signature R/L=1
Pressure signature R/L=1
Pressure at R/L=6
Pressure at R/L=6
Mach iso-values near the spike
Mach iso-values near the spike
Mach iso-values near the spike
Mach iso-values near the spike