shock  viscosity  numerical
problem
What is a shock ?

At the begining of the simulation we disturbe the flow with
a velocity such as : .

The fastest fluid catches up with the slowest one so that
to create a velocity break. This phenomena is called shock.

We can notice that if the disturbance was :the
contrary would have happen : the slope would have decreased.
How can you see the viscosity?

The viscosity tends to erase the disturbance in the flow.
Bigger the viscosity is, faster the disturbance has no more effect.

Following are three results that can show this role.

viscosity = 0.0001 m^{2}/s

The shock appears.

The viscosity makes the difference of velocity decrease till
there is no more break.

viscosity = 0.01 m^{2}/s

The shock tends to appear.

viscosity = 1 m^{2}/s

The viscosity is too big to let the shock appear : the disturbance
is erased as soon as it appears.

We can notice that the following schematics time scale is
smaller than the previous one.
Numerical scattering

This phenomena appears for small values of the viscosity

It produces oscillations oscilation around the shock.

We can notice that the numerical scattering depends on the
numerical variables. It appears sooner (for bigger values of the viscosity)
when
is bigger.
viscosity



0.01 m^{2}/s



0.001 m^{2}/s



0.0001 m^{2}/s


