**Problem
C2.3.**** Analytical 3D
Body of Revolution**

**Overview
**

This problem is aimed at testing
high-order methods for the computation of external flow with a high-order curved
boundary representation in 3D. Inviscid, viscous (laminar) and turbulent flow
conditions will be simulated.

**Governing
Equations**

The governing equations for
inviscid and laminar flows are the 3D Euler and Navier-Stokes
equations with a constant ratio of specific heats of 1.4 and Prandtl number of 0.72. For the laminar flow problem, the
viscosity is assumed a constant.

**Flow
Conditions**

Inviscid: _{ }Laminar: _{ }Turbulent: _{}

**Geometry**

The geometry is a streamlined body based on a 10
percent thick airfoil with boundaries constructed by a surface of revolution.
The airfoil is constructed by an elliptical leading edge and straight lines.

Half
model:

_{}

Figure 3D Body of Revolution

**Reference values**

Reference
area: 0.1 (full model)

Reference
moment length: 1.0

Moment
line: Quarter chord

**Boundary
Conditions**

Far field boundary: Subsonic
inflow and outflow

Wing surface: no slip
adiabatic wall

**Requirements**

1.
Start
the simulation from a uniform free stream everywhere, and monitor the L_{2}
norm of the density residual. Track the work units needed to achieve steady
state. Compute the drag and lift coefficients *c _{d}* and

2.
Perform
grid and order refinement studies to find “converged” *c _{d}* and

3.
Plot
the *c _{d}*
and

4.
Study
the numerical order of accuracy according to *c _{d}* and

5.
Submit
two sets of data to the workshop contact for this case

a)
*c _{d}* and

b)
*c _{d}* and