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6.2  PASS: Poiseuille flow

Author
Stéphane Popinet
Command
sh poiseuille.sh poiseuille.gfs
Version
100416
Required files
poiseuille.gfs (view) (download)
poiseuille.sh error.ref
Running time
4 seconds

A simple parabolic Poiseuille flow in a periodic channel with a constant along-channel acceleration a. The theoretical solution is given by:

u(y)=
a
(1/4−y2)

Figure 87 illustrates the norms of the error between the computed and theoretical solutions as functions of spatial resolution.


Figure 87: Convergence of the error norms as functions of resolution (number of grid points across the channel).

6.2.1  PASS: Poiseuille flow with metric

Author
Stéphane Popinet
Command
sh ../poiseuille.sh metric.gfs
Version
111025
Required files
metric.gfs (view) (download)
error.ref
Running time
11 seconds

A simple Poiseuille flow but using a non-uniformly-stretch metric across the channel. Figure 88 illustrates the norms of the error between the computed and theoretical solutions as functions of spatial resolution.


Figure 88: Convergence of the error norms as functions of resolution (number of grid points across the channel).

6.2.2  PASS: Poiseuille flow with multilayer Saint-Venant

Author
Stéphane Popinet
Command
sh river.sh river.gfs
Version
120620
Required files
river.gfs (view) (download)
river.sh error.ref
Running time

Similar test case but for a half-Poiseuille flow solved using the multi-layer Saint-Venant solver.


Figure 89: Convergence of the error norms as functions of resolution (number of grid points in the channel depth).

6.2.3  PASS: Bagnold flow of a granular material

Author
Pierre-Yves Lagrée
Command
sh ../poiseuille.sh bagnold.gfs
Version
100416
Required files
bagnold.gfs (view) (download)
error.ref
Running time
40 seconds

The flow of a granular material down an inclined plane is simulated using a "µ(I)" rheology. The computed velocity profile is compared with Bagnold’s theoretical solution. Figure 90 illustrates the norms of the error between the computed and theoretical solutions as functions of spatial resolution.


Figure 90: Convergence of the error norms as functions of resolution (number of grid points across the channel).


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