**Problem C1.4.**** Laminar Boundary Layer on a Flat Plate**

**Overview
**

This problem is aimed at testing
high-order methods for viscous boundary layers, where highly clustered meshes
are employed to resolve the steep velocity gradient. The drag coefficient will
be computed, and compared with that obtained with lower order methods.

**Governing
Equations**

The governing equation is the 2D Navier-Stokes equations with a constant ratio of specific
heats of 1.4 and Prandtl number of 0.72. The dynamic
viscosity is also a constant.

**Flow
Conditions**

_{}, angle
of attack _{}, Reynolds
number (based on the plate length) Re_{L} = 1x10^{6}.

**Geometry**

The plate length L is assumed 1.
The computational domain has two other length scales L_{H} and L_{V},
as shown in Figure 1.4. Participants should assess the influence of these
length scales to the numerical results, and select large enough values that the
numerical results are not affected by them.

Figure
1.4.
Computational Domain for the Flat Plate Boundary Layer

**Boundary
Conditions**

As depicted in Figure 1.4.

**Requirements**

1.
A
sensitivity study must be performed to find the appropriate domain size, whose
effect on the drag coefficient is less than 0.01 counts, i.e., 1e-6.

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 drag coefficient *c _{d}*.

3.
Perform
grid and order refinement studies to find a “converged” *c _{d}* value with an error
of 0.01 counts.

4.
Plot
the *c _{d}*
error vs. work units for different

5.
Study
the numerical order of accuracy according to *c _{d}* error vs.

1.
Submit
two sets of data to the workshop contact for this case

a.
*c _{d}* error vs. work
units for different

b.
*c _{d}* error vs