Problem C1.3. Flow over a NACA0012 Airfoil



This problem is aimed at testing high-order methods for the computation of external flow with a high-order curved boundary representation. Both inviscid and viscous, subsonic and transonic flow conditions will be simulated. The transonic problem will also test various methods’ shock capturing ability. The lift and drag coefficients will be computed, and compared with those obtained with lower order methods.


Governing Equations

The governing equation is the 2D Euler and Navier-Stokes equations with a constant ratio of specific heats of 1.4 and Prandtl number of 0.72. For the viscous flow problem, the viscosity is assumed a constant.


Flow Conditions

Three different flow conditions are considered:

a)     Subsonic inviscid flow with , and angle of attack 

b)     Inviscid transonic flow with , and

c)     Subsonic viscous flow with , and  Reynolds number (based on the chord length) Re = 5,000.



The NACA0012 airfoil is defined in the following equation


where . The airfoil defined using this equation has a finite trailing edge of .252%. Various ways exist in the literature to modify this definition such that the trailing edge has a zero thickness. We adopt the one which modifies the  coefficient, i.e.,


The airfoil is shown in the following figure.



Figure 1.3. NACA0012 Airfoil


Boundary Conditions

Far field boundary: subsonic inflow and outflow

Airfoil surface: slip wall for inviscid flow, or no slip adiabatic wall for viscous flow




1.     The results for external flow problems obviously depend on the location of the far field outer boundary and the corresponding boundary condition. A sensitivity study should be performed to find a far field boundary location whose effect on the lift and drag coefficients is less than 0.01 counts, i.e., 1e-6.

2.     Start the simulation from a uniform free stream everywhere, and monitor the L2 norm of the density residual. Compute the work units needed to achieve a steady state. Compute the lift and drag coefficients cl and cd.

3.     Perform hp-refinement studies to find “converged” cl and cd values with an error of 0.01 count.

1.     Plot the cl and cd errors vs. work units for different h and p.

2.     Study the numerical order of accuracy according to cl and cd errors vs.  

3.     Submit two sets of data to the workshop contact for this case

a.      cl and cd errors vs. work units for different h and p

b.     cl and cd errors vs  for different h and p