A linear elastic material (Young's modulus ,
density
,
Poisson's ratio
)
is injected from the left into an initially empty channel.
The material is injected with a speed of .
The length of the channel is
.
We will study results at time
.
At this time the material has filled half of the domain,
so that the density and the velocity should be
in the left
half of the channel, and they should still be zero in the right half of the channel.
A one-dimensional model is used (only a -coordinate).
The filling of the domain is obtained by initializing the
materi_density as an unknown which is to be solved by the
mass conservation law.
We give the calculated density for a finite element mesh
with 32, 64, 128, 256 and 512 linear elements respectively.
Better results correspond to a finer mesh.
It can be seen that on a coarse mesh the density is numerically diffused.
However, the same amount of density is spreaded to the right of
as is
spreaded to the left of
;
this indicates that the numerical algorithm
is conservative.