2.2 PASS:
Convergence of the Poisson solver with solid boundaries
-
Author
- Stéphane Popinet
- Command
- sh circle.sh circle.gfs
- Version
- 1.1.0
- Required files
- circle.gfs (view) (download)
circle.sh res-7.ref error.ref order.ref solution.gfv
- Running time
- 23 seconds
Another of the test cases presented in Popinet [17]. A
circular solid boundary of radius 0.25 is embedded in the
domain. The same right-hand-side is used.
This time the problem does not have an analytical solution and we
use Richardson extrapolation to estimate the error for a given
resolution.
| Figure 9: Solution of the Poisson equation. |
| Figure 10: Evolution of the residual. |
| Figure 11: Average reduction factor. |
| Figure 12: Evolution of the error as a function of resolution. |
| Figure 13: Corresponding convergence order. |
2.2.1 PASS:
Star-shaped solid boundary
-
Author
- Stéphane Popinet
- Command
- sh ../circle.sh star.gfs
- Version
- 1.1.0
- Required files
- star.gfs (view) (download)
res-7.ref error.ref order.ref solution.gfv
- Running time
- 21 seconds
A similar but more difficult test using a star-shaped solid boundary
defined in polar coordinates as
The convergence rate is smaller because the shape of the boundary is
not represented properly on the coarsest levels of the multigrid
hierarchy.
| Figure 14: Solution of the Poisson equation. |
| Figure 15: Evolution of the residual. |
| Figure 16: Average reduction factor. |
| Figure 17: Evolution of the error as a function of resolution. |
| Figure 18: Corresponding convergence order. |
2.2.2 PASS:
Star-shaped solid boundary with refinement
-
Author
- Stéphane Popinet
- Command
- sh ../circle.sh refined.gfs
- Version
- 1.1.2
- Required files
- refined.gfs (view) (download)
res-7.ref error.ref order.ref solution.gfv
- Running time
- 34 seconds
Same as the star test but with two levels of refinement added near
the solid boundary.
| Figure 19: Solution of the Poisson equation. |
| Figure 20: Evolution of the residual. |
| Figure 21: Average reduction factor. |
| Figure 22: Evolution of the error as a function of resolution. |
| Figure 23: Corresponding convergence order. |
2.2.3 PASS:
Thin wall at box boundary
-
Author
- Stéphane Popinet
- Command
- sh ../circle.sh thin.gfs
- Version
- 0.8.0
- Required files
- thin.gfs (view) (download)
res-7.ref error.ref order.ref solution.gfv
- Running time
- 1 minutes 39 seconds
Boxes are used to setup a similar problem but with an infinitely
thin wall.
| Figure 24: Solution of the Poisson equation. |
| Figure 25: Evolution of the residual. |
| Figure 26: Average reduction factor. |
| Figure 27: Evolution of the error as a function of resolution. |
| Figure 28: Corresponding convergence order. |
