Skip to content
Snippets Groups Projects
Verified Commit cb07cd1f authored by Lars Bilke's avatar Lars Bilke
Browse files

[web] Converted to page bundle: remaining elliptic pages.

parent fabdee6d
No related branches found
No related tags found
No related merge requests found
Showing
with 12 additions and 12 deletions
......@@ -104,11 +104,11 @@ info: OGS terminated on 2018-10-12 06:30:13+020
The numerical solution shown in the following picture is almost a linear
gradient:
{{< img src="../square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_VolumetricSourceTerm.png" >}}
{{< img src="square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_VolumetricSourceTerm.png" >}}
The line plot along the $x$ axis shows that the solution is a quadratic
function and is in very good agreement to the analytical solution:
{{< img src="../square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
{{< img src="square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
The difference between the computed solution and the analytical solution is in
the range of machine precision and therefore almost negligible:
{{< img src="../square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
{{< img src="square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
......@@ -118,12 +118,12 @@ A last major part of the output was produced by the linear equation solver (LIS
Compared to the analytical solution presented above the results are very good but in a single point:
{{< img src="../square_1e2_neumann_abs_err.png" >}}
{{< img src="square_1e2_neumann_abs_err.png" >}}
Both Dirichlet boundary conditions are satisfied.
The values of gradients in x direction along the right side and y directions along the top sides of the domain a shown below:
{{< img src="../square_1e2_neumann_gradients.png" >}}
{{< img src="square_1e2_neumann_gradients.png" >}}
The homogeneous Neumann boundary condition on the top side is satisfied (ScalarGradient_Y is close to zero).
The inhomogeneous Neumann boundary condition on the bottom is satisfied only for $y > 0.3$ (where the ScalarGradient_X is close to one) because of incompatible boundary conditions imposed on the bottom right corner of the domain.
......@@ -71,8 +71,8 @@ It will produce some output and write the computed result into a data array of t
### Comparison of the analytical solution and the computed solution
{{< img src="../circle_1e6_gwf_with_nodal_source_term_analytical_solution_head.png" >}}
{{< img src="circle_1e6_gwf_with_nodal_source_term_analytical_solution_head.png" >}}
{{< img src="../circle_1e6_gwf_with_nodal_source_term_diff_analytical_solution_head.png" >}}
{{< img src="circle_1e6_gwf_with_nodal_source_term_diff_analytical_solution_head.png" >}}
{{< img src="../circle_1e6_gwf_with_nodal_source_term_diff_analytical_solution_head_log_scale.png" >}}
{{< img src="circle_1e6_gwf_with_nodal_source_term_diff_analytical_solution_head_log_scale.png" >}}
......@@ -105,7 +105,7 @@ The left figure shows the pressure along the line, in the right figure the
difference between the analytical solution and the numerical calculated solution
is plotted.
{{< img src="../line_1e1_robin_left.png" >}}
{{< img src="line_1e1_robin_left.png" >}}
## Second benchmark: Problem specification and analytical solution
......
......@@ -185,15 +185,15 @@ info: OGS terminated on 2018-10-10 09:22:17+020
### Comparison of the numerical and analytical solutions
{{< img src="../square_1e3_poisson_sin_x_sin_y_sourceterm_Pressure_PythonSourceTerm.png" >}}
{{< img src="square_1e3_poisson_sin_x_sin_y_sourceterm_Pressure_PythonSourceTerm.png" >}}
The above picture shows the numerical result. The solution conforms in the edges
to the prescribed boundary conditions.
{{< img src="../square_1e3_poisson_sin_x_sin_y_sourceterm_Diff_Pressure_AnalyticalSolution_PythonSourceTerm.png" >}}
{{< img src="square_1e3_poisson_sin_x_sin_y_sourceterm_Diff_Pressure_AnalyticalSolution_PythonSourceTerm.png" >}}
Since a coarse mesh ($32 \times 32$ elements) is used for the simulation the
difference between the numerical and the analytical solution is relatively large.
#### Comparison for higher resolution mesh ($316 \times 316$ elements)
{{< img src="../square_1e5_poisson_sin_x_sin_y_sourceterm_Diff_Pressure_AnalyticalSolution_PythonSourceTerm.png" >}}
{{< img src="square_1e5_poisson_sin_x_sin_y_sourceterm_Diff_Pressure_AnalyticalSolution_PythonSourceTerm.png" >}}
The difference between the numerical and the analytical solution is much smaller
than in the coarse mesh case.
0% Loading or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment