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Example 21: Injection of an elastic material into an initially empty channel.

A linear elastic material (Young's modulus $1.e3$, density $1$, Poisson's ratio $0.3$) is injected from the left into an initially empty channel.

\begin{figure}
\centerline {\epsfig{file=ps/ex21dra.ps,width=3cm,angle=-90}}\end{figure}

The material is injected with a speed of $1$. The length of the channel is $1$. We will study results at time $0.5$. At this time the material has filled half of the domain, so that the density and the velocity should be $1$ 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 $x$-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 $0.5$ as is spreaded to the left of $0.5$; this indicates that the numerical algorithm is conservative.

\begin{figure}
\centerline {\epsfig{file=ps/ex21dens.ps,width=5cm}}\end{figure}


next up previous contents
Next: Example 22: Constant volume Up: Examples Previous: Example 20: Three dimensional   Contents
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1999-04-23