By Benoit Seille & Ugo Schuck

Advection-diffusion problem is one of the suitable problem
to check the efficiency of a computational fluid dynamic software. During
this study, we will try

to check the efficiency of STARCD on a advection and
diffusion problem in specific conditions. Therfore we will first introduce
the problem we want to solve with the

advection-diffusion equation, the geometry and boundary
conditions. Then we will see some interesting results to finnaly try to
conclude on the interest of STARCD.

** **The
problem, we want to study is based on the advection-diffusion equation
which is in steady and two-dimensional conditions:

** **The
left terms represent advection which is controled by the velocity, The
right ones represent diffusion controled by conductivity.

**-The Geometry of the Problem**

** **The
geometry of the problem is quite simple, this is a rectangle of about 1m*2m.

**-Condition of the Problem**

the fluid choosen during the study is water. The conditions are summarized is the next figure:

The boundary
conditions are: *four inlet velocity Ux=Uy=u where u depends
on tests.

*two inlet conditions of temperatures T=293 K and concentrtion c=1 (inlet1)

*two inlet conditions of temperatures T=273 K and concentrtion c=0 (inlet2)

*two outlet with pressure conditions P=0 Pa

** **We have
choosen to make our study on a 50*100 cells mesh. The next figure represent
this mesh with velocity inlet conditions:

**-Initialization of the Problem**

The initialization is made with a velocity Ux=Uy=u, T=273 K and c=0 everywhere.

**-Adding a Scalar**

** **The
concentration does not exist as a parameter of STARCD therefore we have
had to generate a passive additional scalar representing concentration.

This operation is easy to do with STARCD.

**-Differencing Schemes**

** **In fact
we use only one scheme, the MARS scheme.

**-Number of Iteration**

** **To validate
the study we will use approximations of diffusion time (Td) and convection
time (Tc) defined by Td=L*L/a and Tc=L/u.

We will now check this estimate time on reults we have obtain with STARCD.

**-The different Scalars**

** **In
this study, there is no differences between results obtained with convection
and diffusion of a temperature or a concentration because both are considered

as passive scalar. They have no influence on the flow.

**-Results**

*Convection leads the flow:

The first test we have made was with an inlet velocity u=1 m/s and a diffusivity a=6.32 E-9 m*m/s. We have obtained the following figure:

__Temperature evolution for u=1 m/s and a=6.32.10^9 m*m/s__

We can see that the flow is quite controled by the advection.
By comparing the diffusion time and the advection time we have found that
the diffusion time 5 millions bigger

than advection time. Therefore we can consider that the
convection leads the flow. However the diffusion seems to have a little
effect on the flow but it can also be numerical

diffusion.

*diffusion leads the flow:

The second test we have made was with a null inlet velocity and a diffusion coefficient a=10 E-5 m*m/s. We have obtained the following result:

__Temperature evolution without advection.__

We can see on the previous figure that it has worked because there is no advection.

During this study, we have spent more time in succeed in the use of STARCD than in obtaining results. In fact, STARCD remains difficult to use.We have just succeed in obtaining some results but it appears clear that our study is not enought efficient to conclude on the resolution of a advection-diffusion problem

with STARCD.

However, this study permited to discover a new computational fluid dynamic software, although it remains difficult to understand well such a complex software in such a short time.