**Problem C3.1.**** Turbulent Flow over a 2D Multi-Element Airfoil**

**Overview
**

This problem is aimed at testing
high-order methods for a two-dimensional turbulent flow with a complex
configuration. It has been
investigated previously with low order methods as part of a NASA Langley
workshop. The target quantity of interest is the lift and drag coefficients at
one free-stream condition, as described below.

**Governing
Equations**

The governing equation is the 2D
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_{∞ }=
0.2, angle of attack α = 16^{o}, Reynolds number (based on the
reference chord) Re = 9x10^{6}.
The boundary layer is assumed fully turbulent and no wind tunnel effects
are to be modeled.

**Geometry**

The multi-element airfoil
geometry is shown in the following figure. Originally the geometry is defined
with a set of points. These points are then used to define a
high-order geometry, which will be available online at the workshop web
site.

The reference chord length is
0.5588 m.

Figure 3.1. MDA 30P-30N multi-element airfoil geometry

**Boundary
Conditions**

Adiabatic
no-slip wall on the airfoil surface, free-stream at the farfield.

**Grids**

Participants may use their own
grids for the convergence study. In this case, the geometry definition provided
at the workshop web site should be used such that all the participants will use
the same geometry. The workshop will also provide sample high-order
computational meshes.

**Requirements**

1.
Perform
a convergence study of drag and lift coefficient, *c _{l}* and

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
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 _{l}* &

b. *c _{l}* &

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