**Problem C3.2.**** Turbulent Flow over the DPW III Wing Alone Case**

**Overview
**

This problem is aimed at testing
high-order methods for a three-dimensional wing case with turbulent boundary
layers at transonic conditions.
This problem has been investigated previously with low order methods as
part of the AIAA drag prediction workshop,

http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw/Workshop3/

(see
DPW-W1). The target quantity of
interest is the drag coefficient at one free-stream condition, as described
below.

**Governing
Equations**

The governing equation is the 3D
Reynolds-averaged Navier-Stokes equations with a
constant ratio of specific heats of 1.4 and Prandtl
number of 0.71. The dynamic viscosity is also a constant. The choice of turbulence model is left
up to the participants; recommended suggestions are 1) the Spalart
Allmaras model, and 2) the Wilcox k-omega model.

**Flow
Conditions**

Mach number M_{∞}=0.76,
angle of attack α=0.5^{o}, Reynolds number (based on the reference
chord) Re_{cref} = 5x10^{6}. The boundary layer is assumed fully
turbulent and no wind tunnel effects are to be modeled.

**Geometry**

The wing geometry, illustrated
below with pressure contours, is available online at

http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw/Workshop3/DPW3-geom.html

The reference quantities are as
follows:

Planform area: S_{ref} = 290322 mm^{2} = 450 in^{2}

Chord: c_{ref} = 197.556 mm = 7.778 in

Span: b
= 1524 mm = 60 in

**Boundary
Conditions**

Adiabatic
no-slip wall on the wing, symmetry at the wing root, and free-stream at the farfield.

**Grids**

Participants may use their own
grids for the convergence study.
The initial coarse mesh should yield similar geometry *resolution *to the coarse meshes provided
by the DPW workshop:

http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw/Workshop3/grids.html

The grids provided by the
workshop, as well as the gridding guidelines,

http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw/Workshop3/gridding_guidelines.html

are understood to
be relevant to second-order methods.
Grids for higher-order methods will likely be coarser for the same level
of solution accuracy. However, the
geometry must still be represented accurately. For example if curved elements are used,
the maximum error in the geometry representation should be similar to the error
in the finer linear meshes. For
structured meshes, one technique for achieving this resolution requirement is
to agglomerate linear elements from the low-order meshes into higher-order, curved, macro-elements.
For example a 3x3 block of linear elements can be combined into one
cubic curved element, yielding 27 times fewer elements at a similar geometry
resolution.

**Requirements**

1.
Perform
a convergence study of drag coefficient, *c _{d}*, using one or more
of the following three techniques:

a.
Uniform
mesh refinement of the coarsest mesh

b.
Quasi-uniform
refinement of the coarsest mesh, in which the meshes are not necessarily nested
but in which the relative grid density throughout the domain is constant.

c.
Adaptive
refinement using an error indicator (e.g. output-based).

Record the degrees of freedom and
the work units for each data point, where the CPU t=0 corresponds to
initialization with free-stream conditions on the coarsest mesh.

2.
Submit
two sets of data to the workshop contact for this case

a. *c _{d}* error versus work
units

b. *c _{d}* error versus
degrees of freedom

Include a
description of the coarsest mesh resolution and of the strategy used for
refinement.