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Verified Commit cb07cd1f authored by Lars Bilke's avatar Lars Bilke
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[web] Converted to page bundle: remaining elliptic pages.

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...@@ -104,11 +104,11 @@ info: OGS terminated on 2018-10-12 06:30:13+020 ...@@ -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 The numerical solution shown in the following picture is almost a linear
gradient: 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 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: 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 difference between the computed solution and the analytical solution is in
the range of machine precision and therefore almost negligible: 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 ...@@ -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: 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. 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: 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 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. 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 ...@@ -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 ### 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 ...@@ -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 difference between the analytical solution and the numerical calculated solution
is plotted. is plotted.
{{< img src="../line_1e1_robin_left.png" >}} {{< img src="line_1e1_robin_left.png" >}}
## Second benchmark: Problem specification and analytical solution ## Second benchmark: Problem specification and analytical solution
......
...@@ -185,15 +185,15 @@ info: OGS terminated on 2018-10-10 09:22:17+020 ...@@ -185,15 +185,15 @@ info: OGS terminated on 2018-10-10 09:22:17+020
### Comparison of the numerical and analytical solutions ### 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 The above picture shows the numerical result. The solution conforms in the edges
to the prescribed boundary conditions. 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 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. difference between the numerical and the analytical solution is relatively large.
#### Comparison for higher resolution mesh ($316 \times 316$ elements) #### 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 The difference between the numerical and the analytical solution is much smaller
than in the coarse mesh case. than in the coarse mesh case.
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