**Problem C1.3.**** Flow over a NACA0012 Airfoil**

**Overview **

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.

**Geometry**

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

**Requirements**

1. If you generate new meshes, please adhere to the following guideline: The far field should be a circle, centered at the airfoil mid chord with a radius of 1000 chords. Do not apply any vortex correction at the far field.

2. Start
the simulation from a uniform free stream everywhere, and monitor the L_{2} norm of the density residual. Compute the work units needed to achieve a steady
state. Compute the lift and drag coefficients *c _{l}* and

3. Perform
hp-refinement studies to find ¡°converged¡± *c _{l}* and

1. Plot
the *c _{l}* and

2. Study
the numerical order of accuracy according to *c _{l}* and

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

a. *c _{l}* and

b. *c _{l}* and