**Problem C2.4.**** Laminar Flow around a Delta Wing**

**Overview **

A laminar flow
at high angle of attack around a delta wing with a sharp leading edge and a
blunt trailing edge. As the flow passes the leading edge it rolls up and
creates a vortex together with a secondary vortex. The vortex system remains
over a long distance behind the wing. This problem is aimed at testing
high-order and adaptive methods for the computation of vortex dominated
external flows. Note, that methods which show high-order on smooth solutions
will show about 1^{st} order only on this test case because of reduced
smoothness properties (e.g. at the sharp edges) of the flow solution. Finally,
also h-adaptive, and hp-adaptive computations can be
submitted for this test case.

**Governing
Equations**

The governing equation is the 3D Navier-Stokes equations with a constant ratio of specific heats of 1.4 and Prandtl number of 0.72. The viscosity is assumed a constant.

**Flow
Conditions**

Subsonic viscous flow with M_{¡Þ}= 0.3, and ¦Á =
12.5¡ã, Reynolds number (based on a mean cord length of 1) Re=4000.

**Geometry**

The geometry is a delta wing with a sloped and sharp leading edge and a blunt trailing edge. The geometry can be seen from Fig. 5 which shows the top, bottom and side view of the half model of the delta wing.

Half model:

Figure 4: Left: Top, bottom and side view of the half model of the delta wing. The grid has been provided by NLR within the ADIGMA project. Right: Streamlines and Mach number isosurfaces of the flow solution over the left half of the wing and Mach number slices over the right half. The figures are taken from [LH10].

**Reference values**

Reference area: 0.133974596 (half model)

Reference moment length: 1.0

Moment line: Quarter chord

**Boundary
Conditions**

Far field boundary: Subsonic inflow and outflow

Wing surface: no slip
isothermal wall with _{}.

**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

6. The following data sets can also be submitted

a. for sequences of locally refined meshes (h-adaptive mesh refinement) and

b. for sequences of meshes with locally varying mesh
size and order of convergence (hp-adaptive mesh refinement), possibly including
improved data based on *a posteriori* error estimation results.

Note, that here the error-vs-work-unit data sets should take account of the additional work units possibly required

- for auxiliary problems (like e.g. adjoint problems),

- for the evaluation of refinement indicators or mesh metrics,

- and for the actual mesh refinement or mesh regeneration procedure.

**References**

[LH10] T. Leicht and R. Hartmann. Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations. J. Comput. Phys., 229(19), 7344-7360, 2010.