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7.2  PASS: Flow through a divergent channel

Author
Stéphane Popinet
Command
sh channel.sh channel.gfs
Version
1.1.0
Required files
channel.gfs (view) (download)
channel.sh orderU.ref orderfU.ref orderV.ref orderfV.ref
Running time
3 minutes 35 seconds

A test case initially presented by Almgren et al [2]. The Euler equations are solved in a divergent channel for a unit inflow velocity on the left boundary and outflow on the right boundary.

Tables 7 and 8 illustrate the errors and convergence orders obtained for both components of the velocity when the resolution varies. Richardson extrapolation is used. The errors are computed either on the whole domain (All cells) or on the cells whose parents at level 5 are entirely contained in the fluid (Full 128 cells).

Close to second-order convergence is obtained in the bulk of the fluid, reducing to first-order close to the boundaries. The errors are small in all cases (with a maximum of .5%) and comparable to that obtained by Almgren et al using a different discretisation.


Table 7: Errors and convergence rates for the x-component of the velocity.
 All cellsFull 128 cells
 128-256Rate256-512128-256Rate256-512
L11.18e-041.215.09e-051.02e-041.453.74e-05
 1.18e-041.215.09e-051.02e-041.453.74e-05
L22.89e-040.901.54e-042.58e-041.191.13e-04
 2.89e-040.901.54e-042.58e-041.191.13e-04
L2.33e-030.531.62e-032.18e-030.681.36e-03
 2.33e-030.531.62e-032.18e-030.681.36e-03


Table 8: Errors and convergence rates for the y-component of the velocity.
 All cellsFull 128 cells
 128-256Rate256-512128-256Rate256-512
L11.73e-041.824.90e-051.54e-042.173.42e-05
 1.73e-041.824.90e-051.54e-042.173.42e-05
L25.27e-041.461.91e-044.97e-041.801.43e-04
 5.27e-041.461.91e-044.97e-041.801.43e-04
L4.55e-030.912.43e-034.55e-031.002.28e-03
 4.55e-030.912.43e-034.55e-031.002.28e-03


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