Case description


  • 2D structured mesh created using blockMesh
  • bump described

    \[y(x) = \begin{cases} 0.05 [\sin(\pi \frac{x}{0.9}-\frac{\pi}{3})]^4, & 0.3 \le x \le 1.2, \\ 0 , & 0 \le x \lt 0.3 \, \text{and} \, 1.2 \lt x \le 1.5. \end{cases}\]
  • this has been set in the blockMeshDict using a codeStream

Close-up around the bump

Boundary conditions

  • \(U\) based on a Mach number of 0.2. Mach number, \(Ma\), is defined as:

    \[Ma = \sqrt{\gamma R T}\]

    where \(\gamma\) is the ratio of specific heats, \(R\) the gas constant and \(T\) the temperature. Using values for air at 300K, the inflow velocity is given as:

    \[U = 0.2 Ma = 0.2 \sqrt{1.4 \times 287 \times 300} = 69.44 m/s\]
  • The laminar viscosity is derived from the Reynolds number, i.e.

    \[\nu_\infty = \frac{|\u| L}{Re} = \frac{69.44 \times 1}{3 \times 10^6} = 2.31 \times 10^{-5} m^2/s\]

Common fields

Velocity: U

Patch Condition Value
Inlet fixedValue 69.44 m/s in x
Outlet zeroGradient  
Bump noSlip  
Walls symmetryPlane  

Pressure: p

Patch Condition Value
Inlet zeroGradient  
Outlet fixedValue 0 Pa (static)
Bump zeroGradient  
Walls symmetryPlane  

Turbulence fields

Turbulence viscosity: nut

Patch Condition Value
Inlet calculated  
Outlet calculated  
Bump nutUSpaldingWallFunction  
Walls symmetryPlane  


Modified turbulence viscosity: nuTilda

Patch Condition Value
Inlet fixedValue based on \(3 \nu_\infty\)
Outlet zeroGradient  
Bump fixedValue 0
Walls symmetryPlane  


The NASA Turbulence Modelling Resource employs a code comparison to show that the FUN3D and CFL3D codes produce equivalent results for this case. OpenFOAM and CFL3D results are presented in the following series of images, showing that OpenFOAM results compare very favourably.

Normalised turbulence viscosity  
Skin friction Pressure coefficient