From dde3e3c050013e240a4d737722b4dac07d818da0 Mon Sep 17 00:00:00 2001
From: Thomas Fischer <thomas.fischer@ufz.de>
Date: Tue, 25 Sep 2018 08:52:24 +0200
Subject: [PATCH] [Docu/web] Add volumetric source term docu.

---
 ...ow-dirichlet-volumetric-source-term.pandoc | 111 ++++++++++++++++++
 ...nalyticalSolution_VolumetricSourceTerm.png |   3 +
 ...nalyticalSolution_VolumetricSourceTerm.png |   3 +
 3 files changed, 117 insertions(+)
 create mode 100644 web/content/docs/benchmarks/elliptic/groundwater-flow-dirichlet-volumetric-source-term.pandoc
 create mode 100644 web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
 create mode 100644 web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png

diff --git a/web/content/docs/benchmarks/elliptic/groundwater-flow-dirichlet-volumetric-source-term.pandoc b/web/content/docs/benchmarks/elliptic/groundwater-flow-dirichlet-volumetric-source-term.pandoc
new file mode 100644
index 00000000000..50905f96bde
--- /dev/null
+++ b/web/content/docs/benchmarks/elliptic/groundwater-flow-dirichlet-volumetric-source-term.pandoc
@@ -0,0 +1,111 @@
++++
+date = "2018-09-25T08:17:39+01:00"
+title = "Groundwater Flow (Volumetric Source Term)"
+project = "Elliptic/square_1x1_GroundWaterFlow/square_1e2_volumetricsourceterm.prj"
+author = "Tom Fischer"
+weight = 102
+
+aliases = [ "/docs/benchmarks/" ] # First benchmark page
+
+[menu]
+  [menu.benchmarks]
+    parent = "elliptic"
+
++++
+
+{{< data-link >}}
+
+## Equations
+
+We start with Poisson equation:
+$$
+\begin{equation}
+k\; \Delta p = Q \quad \text{in }\Omega
+\end{equation}$$
+w.r.t boundary conditions
+$$
+\eqalign{
+p(x) = g_D(x) &\quad \text{on }\Gamma_D,\cr
+k\;{\partial p(x) \over \partial n} = g_N(x) &\quad \text{on }\Gamma_N,
+}$$
+
+where $p$ could be the pressure, the subscripts $D$ and $N$ denote the Dirichlet- and Neumann-type boundary conditions, $n$ is the normal vector pointing outside of $\Omega$, and $\Gamma = \Gamma_D \cup \Gamma_N$ and $\Gamma_D \cap \Gamma_N = \emptyset$.
+
+## Problem specification and analytical solution
+
+We solve the Poisson equation on a square domain $[0\times 1]^2$ with $k = 1$ w.r.t. the specific boundary conditions:
+$$
+\eqalign{
+p(x,y) = 2 &\quad \text{on } (x=0,y) \subset \Gamma_D,\cr
+p(x,y) = 1 &\quad \text{on } (x=1,y) \subset \Gamma_D,\cr
+k\;{\partial p(x,y) \over \partial n} = 0 &\quad \text{on }\Gamma_N.
+}$$
+and the source term is $Q=1$.
+
+The solution of this problem is
+$$
+p(x,y) = - \frac{1}{2} (x^2 + x) + 2.
+$$
+
+## Input files
+
+The main project file is `square_1e2_volumetricsourceterm.prj`. It describes the
+processes to be solved and the related process variables together with their
+initial and boundary conditions. It also references the bulk mesh and the
+boundary meshes associated with the bulk mesh.
+
+The input mesh `square_1x1_quad_1e2.vtu` is stored in the VTK file format and can be directly visualized in Paraview for example.
+
+## Running simulation
+
+To start the simulation (after successful compilation) run:
+```bash
+$ ogs square_1e2_volumetricsourceterm.prj
+```
+
+It will produce some output and write the computed result into the
+`square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000.vtu`, which can be
+directly visualized and analysed in paraview for example.
+
+The output on the console will be similar to the following on:
+```
+info: ConstantParameter: K
+info: ConstantParameter: p0
+info: ConstantParameter: p_Dirichlet_left
+info: ConstantParameter: p_Dirichlet_right
+info: ConstantParameter: volumetric_source_term_parameter
+info: Initialize processes.
+info: Solve processes.
+info: [time] Output of timestep 0 took 0.000408888 s.
+info: === Time stepping at step #1 and time 1 with step size 1
+info: [time] Assembly took 0.000366926 s.
+info: [time] Applying Dirichlet BCs took 3.76701e-05 s.
+info: ------------------------------------------------------------------
+info: *** Eigen solver computation
+info: -> solve with CG (precon DIAGONAL)
+info:    iteration: 9/10000
+info:    residual: 7.661918e-17
+
+info: ------------------------------------------------------------------
+info: [time] Linear solver took 0.000194073 s.
+info: [time] Iteration #1 took 0.000657082 s.
+info: [time] Solving process #0 took 0.000686884 s in time step #1
+info: [time] Time step #1 took 0.000750065 s.
+info: [time] Output of timestep 1 took 0.000280857 s.
+info: The whole computation of the time stepping took 1 steps, in which
+         the accepted steps are 1, and the rejected steps are 0.
+
+info: [time] Execution took 0.0493069 s.
+info: OGS terminated on 2018-09-25 08:00:58+020
+```
+
+## Results and evaluation
+
+### Comparison of the analytical solution and the computed solution
+
+{{< img src="../square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
+There is no visible difference between the computed pressure and the analytical
+solution.
+{{< img src="../square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
+The difference between the pressure and the analytical solution is the range of
+machine accuracy.
diff --git a/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
new file mode 100644
index 00000000000..ab8c1bb6438
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+++ b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
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+size 16954
diff --git a/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
new file mode 100644
index 00000000000..ee61773b549
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+++ b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
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+size 11378
-- 
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