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 0000000000000000000000000000000000000000..50905f96bde94a073e0204333462c4502108eba1 --- /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 0000000000000000000000000000000000000000..ab8c1bb643872e7a4470e8065e68906c635cc841 --- /dev/null +++ b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3c063b973e6e2aef887077ab627ba273727ccd6d4ae964d27cfc25779972532b +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 0000000000000000000000000000000000000000..ee61773b549609b6a470bcaed49e390ab3de7898 --- /dev/null +++ b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c8df95d8054c45644cfc9f6185b2c9a120fedf51c400bc6dd8e450ba80313bfd +size 11378