From f4af587fd5fac224d4a287dc1a2238a4b2619796 Mon Sep 17 00:00:00 2001 From: Marc Walther <marc.walther@ufz.de> Date: Thu, 2 May 2019 14:29:50 +0200 Subject: [PATCH] Add Theis Benchmark for ComponentTransport --- ProcessLib/ComponentTransport/Tests.cmake | 44 +++ .../ComponentTransport/HC_Theis/HC_theis.prj | 302 ++++++++++++++++++ .../HC_Theis/abstraction_whole_surf.vtu | 3 + .../HC_Theis/analytical_theis.xlsx | Bin 0 -> 332354 bytes .../HC_Theis/drawdown_s-30.txt | 25 ++ .../HC_Theis/drawdown_t-5e3.txt | 202 ++++++++++++ .../HC_Theis/inflow_surf.vtu | 3 + .../out_HC_theis_pcs_0_ts_0_t_0.000000.vtu | 3 + .../out_HC_theis_pcs_0_ts_10_t_100.000000.vtu | 3 + .../out_HC_theis_pcs_0_ts_20_t_400.000000.vtu | 3 + ...out_HC_theis_pcs_0_ts_30_t_1000.000000.vtu | 3 + ...out_HC_theis_pcs_0_ts_40_t_2000.000000.vtu | 3 + ...out_HC_theis_pcs_0_ts_50_t_5000.000000.vtu | 3 + ...ut_HC_theis_pcs_0_ts_60_t_20000.000000.vtu | 3 + ...ut_HC_theis_pcs_0_ts_70_t_70000.000000.vtu | 3 + ...t_HC_theis_pcs_0_ts_73_t_100000.000000.vtu | 3 + .../HC_Theis/slice_reorder.vtu | 3 + .../benchmarks/hydro-component/theis/BCs.png | 3 + .../hydro-component/theis/HC_Theis.pandoc | 65 ++++ .../hydro-component/theis/comparison.png | 3 + 20 files changed, 680 insertions(+) create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/HC_theis.prj create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/abstraction_whole_surf.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/analytical_theis.xlsx create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/drawdown_s-30.txt create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/drawdown_t-5e3.txt create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/inflow_surf.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/out_HC_theis_pcs_0_ts_0_t_0.000000.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/out_HC_theis_pcs_0_ts_10_t_100.000000.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/out_HC_theis_pcs_0_ts_20_t_400.000000.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/out_HC_theis_pcs_0_ts_30_t_1000.000000.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/out_HC_theis_pcs_0_ts_40_t_2000.000000.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/out_HC_theis_pcs_0_ts_50_t_5000.000000.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/out_HC_theis_pcs_0_ts_60_t_20000.000000.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/out_HC_theis_pcs_0_ts_70_t_70000.000000.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/out_HC_theis_pcs_0_ts_73_t_100000.000000.vtu create mode 100644 Tests/Data/Parabolic/ComponentTransport/HC_Theis/slice_reorder.vtu create mode 100644 web/content/docs/benchmarks/hydro-component/theis/BCs.png create mode 100644 web/content/docs/benchmarks/hydro-component/theis/HC_Theis.pandoc create mode 100644 web/content/docs/benchmarks/hydro-component/theis/comparison.png diff --git a/ProcessLib/ComponentTransport/Tests.cmake b/ProcessLib/ComponentTransport/Tests.cmake index b7e977d61dc..91dd68099a6 100644 --- a/ProcessLib/ComponentTransport/Tests.cmake +++ b/ProcessLib/ComponentTransport/Tests.cmake @@ -853,3 +853,47 @@ AddTest( vdbc_pcs_0_ts_21990_t_210000.000000_expected.vtu vdbc_pcs_0_ts_21990_t_210000.000000.vtu concentration Si 1e-5 1e-4 vdbc_pcs_0_ts_25990_t_250000.000000_expected.vtu vdbc_pcs_0_ts_25990_t_250000.000000.vtu concentration Si 1e-5 1e-4 ) + +AddTest( + NAME HC_Theis + PATH Parabolic/ComponentTransport/HC_Theis + EXECUTABLE ogs + EXECUTABLE_ARGS HC_theis.prj + WRAPPER time + TESTER vtkdiff + REQUIREMENTS NOT OGS_USE_MPI + RUNTIME 90 + DIFF_DATA + out_HC_theis_pcs_0_ts_0_t_0.000000.vtu + out_HC_theis_pcs_0_ts_0_t_0.000000.vtu pressure pressure 1e-3 1e-6 + out_HC_theis_pcs_0_ts_0_t_0.000000.vtu + out_HC_theis_pcs_0_ts_0_t_0.000000.vtu darcy_velocity darcy_velocity 1e-10 1e-6 + out_HC_theis_pcs_0_ts_10_t_100.000000.vtu + out_HC_theis_pcs_0_ts_10_t_100.000000.vtu pressure pressure 1e-3 1e-6 + out_HC_theis_pcs_0_ts_10_t_100.000000.vtu + out_HC_theis_pcs_0_ts_10_t_100.000000.vtu darcy_velocity darcy_velocity 1e-10 1e-6 + out_HC_theis_pcs_0_ts_20_t_400.000000.vtu + out_HC_theis_pcs_0_ts_20_t_400.000000.vtu pressure pressure 1e-3 1e-6 + out_HC_theis_pcs_0_ts_20_t_400.000000.vtu + out_HC_theis_pcs_0_ts_20_t_400.000000.vtu darcy_velocity darcy_velocity 1e-10 1e-6 + out_HC_theis_pcs_0_ts_30_t_1000.000000.vtu + out_HC_theis_pcs_0_ts_30_t_1000.000000.vtu pressure pressure 1e-3 1e-6 + out_HC_theis_pcs_0_ts_30_t_1000.000000.vtu + out_HC_theis_pcs_0_ts_30_t_1000.000000.vtu darcy_velocity darcy_velocity 1e-10 1e-6 + out_HC_theis_pcs_0_ts_40_t_2000.000000.vtu + out_HC_theis_pcs_0_ts_40_t_2000.000000.vtu pressure pressure 1e-3 1e-6 + out_HC_theis_pcs_0_ts_40_t_2000.000000.vtu + out_HC_theis_pcs_0_ts_40_t_2000.000000.vtu darcy_velocity darcy_velocity 1e-10 1e-6 + out_HC_theis_pcs_0_ts_60_t_20000.000000.vtu + out_HC_theis_pcs_0_ts_60_t_20000.000000.vtu pressure pressure 1e-3 1e-6 + out_HC_theis_pcs_0_ts_60_t_20000.000000.vtu + out_HC_theis_pcs_0_ts_60_t_20000.000000.vtu darcy_velocity darcy_velocity 1e-10 1e-6 + out_HC_theis_pcs_0_ts_70_t_70000.000000.vtu + out_HC_theis_pcs_0_ts_70_t_70000.000000.vtu pressure pressure 1e-3 1e-6 + out_HC_theis_pcs_0_ts_70_t_70000.000000.vtu + out_HC_theis_pcs_0_ts_70_t_70000.000000.vtu darcy_velocity darcy_velocity 1e-10 1e-6 + out_HC_theis_pcs_0_ts_73_t_100000.000000.vtu + out_HC_theis_pcs_0_ts_73_t_100000.000000.vtu pressure pressure 1e-3 1e-6 + out_HC_theis_pcs_0_ts_73_t_100000.000000.vtu + out_HC_theis_pcs_0_ts_73_t_100000.000000.vtu darcy_velocity darcy_velocity 1e-10 1e-6 +) \ No newline at end of file diff --git a/Tests/Data/Parabolic/ComponentTransport/HC_Theis/HC_theis.prj b/Tests/Data/Parabolic/ComponentTransport/HC_Theis/HC_theis.prj new file mode 100644 index 00000000000..f5ec6c80e0c --- /dev/null +++ b/Tests/Data/Parabolic/ComponentTransport/HC_Theis/HC_theis.prj @@ -0,0 +1,302 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<OpenGeoSysProject> + <meshes> + <mesh>slice_reorder.vtu</mesh> + <mesh>inflow_surf.vtu</mesh> + <mesh>abstraction_whole_surf.vtu</mesh> + </meshes> + + <processes> + <process> + <name>ComponentTransport</name> + <type>ComponentTransport</type> + <integration_order>2</integration_order> + <process_variables> + <concentration>concentration</concentration> + <pressure>pressure</pressure> + </process_variables> + <secondary_variables> + <secondary_variable type="static" internal_name="darcy_velocity" output_name="darcy_velocity"/> + </secondary_variables> + <!-- <calculatesurfaceflux> + <mesh>abstraction_whole_surf</mesh> + <property_name>flux</property_name> + <output_mesh>out_abstraction_whole_surf_flux.vtu</output_mesh> + </calculatesurfaceflux> --> + <fluid> + <density> + <type>ConcentrationAndPressureDependent</type> + <fluid_density_concentration_difference_ratio>0</fluid_density_concentration_difference_ratio> + <fluid_density_pressure_difference_ratio>5.0968E-08</fluid_density_pressure_difference_ratio> + <reference_concentration>0</reference_concentration> + <reference_pressure>0</reference_pressure> + <reference_density>1000</reference_density> + </density> + <viscosity> + <type>Constant</type> + <value>1.0e-3</value> + </viscosity> + </fluid> + <porous_medium> + <porous_medium id="0"> + <permeability> + <type>Constant</type> + <permeability_tensor_entries>kappa1</permeability_tensor_entries> + </permeability> + <porosity> + <type>Constant</type> + <porosity_parameter>porosity1</porosity_parameter> + </porosity> + <!-- The implementation of the ComponentTransport process + is without Boussinesq approximations, thus, 'storage' is not + used here, but should be set through S = thickness * gravity * porosity * d\rho / dp / rho. --> + <storage> + <type>Constant</type> + <value>0</value> + </storage> + </porous_medium> + </porous_medium> + <fluid_reference_density>rho_fluid</fluid_reference_density> + <retardation_factor>retardation</retardation_factor> + <decay_rate>decay</decay_rate> + <specific_body_force>0 0 -9.81</specific_body_force> + </process> + </processes> + <media> + <medium id="0"> + <phases> + <phase> + <type>AqueousLiquid</type> + <components> + <component> + <name>concentration</name> + <properties> + <property> + <name>molecular_diffusion</name> + <type>Constant</type> + <value>2e-9</value> + </property> + </properties> + </component> + </components> + </phase> + </phases> + <properties> + <property> + <name>longitudinal_dispersivity</name> + <type>Constant</type> + <value>0</value> + </property> + <property> + <name>transversal_dispersivity</name> + <type>Constant</type> + <value>0</value> + </property> + </properties> + </medium> + </media> + <time_loop> + <processes> + <process ref="ComponentTransport"> + <nonlinear_solver>basic_picard</nonlinear_solver> + <convergence_criterion> + <type>PerComponentDeltaX</type> + <norm_type>NORM2</norm_type> + <reltols>1e-5 5e-6</reltols> + </convergence_criterion> + <time_discretization> + <type>BackwardEuler</type> + </time_discretization> + <time_stepping> + <type>FixedTimeStepping</type> + <t_initial> 0.0 </t_initial> + <t_end> 1e5 </t_end> + <timesteps> + <pair> + <repeat>10</repeat> + <delta_t>10</delta_t> + </pair> + <pair> + <repeat>5</repeat> + <delta_t>20</delta_t> + </pair> + <pair> + <repeat>10</repeat> + <delta_t>40</delta_t> + </pair> + <pair> + <repeat>5</repeat> + <delta_t>80</delta_t> + </pair> + <pair> + <repeat>10</repeat> + <delta_t>100</delta_t> + </pair> + <pair> + <repeat>5</repeat> + <delta_t>200</delta_t> + </pair> + <pair> + <repeat>5</repeat> + <delta_t>400</delta_t> + </pair> + <pair> + <repeat>5</repeat> + <delta_t>1000</delta_t> + </pair> + <pair> + <repeat>5</repeat> + <delta_t>2000</delta_t> + </pair> + <pair> + <repeat>10</repeat> + <delta_t>5000</delta_t> + </pair> + <pair> + <repeat>5</repeat> + <delta_t>10000</delta_t> + </pair> + <pair> + <repeat>5</repeat> + <delta_t>20000</delta_t> + </pair> + </timesteps> + </time_stepping> + </process> + </processes> + <output> + <type>VTK</type> + <prefix>out_HC_theis</prefix> + <timesteps> + <pair> + <repeat> 1 </repeat> + <each_steps> 10 </each_steps> + </pair> + </timesteps> + <variables> + <variable> pressure </variable> + <variable> concentration </variable> + <variable> darcy_velocity </variable> + </variables> + </output> + </time_loop> + + <parameters> + <parameter> + <name>rho_fluid</name> + <type>Constant</type> + <value>1000</value> + </parameter> + <parameter> + <name>retardation</name> + <type>Constant</type> + <value>1</value> + </parameter> + <parameter> + <name>decay</name> + <type>Constant</type> + <value>0</value> + </parameter> + + <parameter> + <name>porosity1</name> + <type>Constant</type> + <value>0.2</value> + </parameter> + <parameter> + <name>kappa1</name> + <type>Constant</type> + <values>7.6453E-13 0 0 0 7.6453E-13 0 0 0 7.6453E-13</values> + </parameter> + + <parameter> + <name>c_ini</name> + <type>MeshNode</type> + <mesh>slice_reorder</mesh> + <field_name>c_ini</field_name> + </parameter> + <parameter> + <name>p_ini</name> + <type>MeshNode</type> + <mesh>slice_reorder</mesh> + <field_name>p_ini</field_name> + </parameter> + <parameter> + <name>c_0</name> + <type>Constant</type> + <value>0</value> + </parameter> + <parameter> + <name>p_BC_Dirichlet</name> + <type>MeshNode</type> + <mesh>inflow_surf</mesh> + <field_name>p_BC_Dirichlet</field_name> + </parameter> + <parameter> + <name>p_BC_Neumann_c</name> + <type>Constant</type> + <value>-2.83542E-03</value> + </parameter> + + + </parameters> + + <process_variables> + <process_variable> + <name>concentration</name> + <components>1</components> + <order>1</order> + <initial_condition>c_ini</initial_condition> + <boundary_conditions> + <boundary_condition> + <type>Dirichlet</type> + <mesh>inflow_surf</mesh> + <parameter>c_0</parameter> + </boundary_condition> + </boundary_conditions> + </process_variable> + <process_variable> + <name>pressure</name> + <components>1</components> + <order>1</order> + <initial_condition>p_ini</initial_condition> + <boundary_conditions> + <boundary_condition> + <type>Dirichlet</type> + <mesh>inflow_surf</mesh> + <parameter>p_BC_Dirichlet</parameter> + </boundary_condition> + <boundary_condition> + <type>Neumann</type> + <mesh>abstraction_whole_surf</mesh> + <parameter>p_BC_Neumann_c</parameter> + </boundary_condition> + </boundary_conditions> + </process_variable> + </process_variables> + + <nonlinear_solvers> + <nonlinear_solver> + <name>basic_picard</name> + <type>Picard</type> + <max_iter>30</max_iter> + <linear_solver>general_linear_solver</linear_solver> + </nonlinear_solver> + </nonlinear_solvers> + <linear_solvers> + <linear_solver> + <name>general_linear_solver</name> + <lis>-i cg -p jacobi -tol 1e-10 -maxiter 10000</lis> + <eigen> + <solver_type>CG</solver_type> + <precon_type>DIAGONAL</precon_type> + <max_iteration_step>10000</max_iteration_step> + <error_tolerance>1e-10</error_tolerance> + </eigen> + <petsc> + <prefix>lf</prefix> + <parameters>-lf_ksp_type cg -lf_pc_type bjacobi -lf_ksp_rtol 1e-16 -lf_ksp_max_it 10000</parameters> + </petsc> + </linear_solver> + </linear_solvers> +</OpenGeoSysProject> diff --git a/Tests/Data/Parabolic/ComponentTransport/HC_Theis/abstraction_whole_surf.vtu b/Tests/Data/Parabolic/ComponentTransport/HC_Theis/abstraction_whole_surf.vtu new file mode 100644 index 00000000000..79c0ff13078 --- /dev/null +++ b/Tests/Data/Parabolic/ComponentTransport/HC_Theis/abstraction_whole_surf.vtu @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid 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For a sustainable water usage, the evaluation of the spatio-temporal behaviour of the water level for a specified abstraction rate is of high importance for water management. + +This benchmark verifies the groundwater level drawdown for an aquifer that is subjected to pumping. + + +## Problem description + +For pumping from a well, Theis (1935) proposed an analytical solution to calculate the water level drawdown over time and distance from the well. A short summary of the solution can be seen in +web/content/docs/benchmarks/liquid-flow/liquid-flow-theis-problem.pandoc + +Here, we verify pumping abstraction with Theis for the `ComponentTransport` process using a 3D setup. The setup is adapted from Walther (2014), section 3.2. + + +### Model setup + +The setup comprises a 1/8th slice of a full circle (see figure 1). + +{{< img src="../BCs.png" title="Mesh and boundary conditions (BC); blue = outer Dirichlet pressure and concentration BC, red = inner Neumann abstraction BC.">}} + +The outer boundary condition is set as Dirichlet with a hydrostatic pressure along the shell surface of the slice equivalent to a head of $h = 0 m$ (i.e. water level equals top of domain). For mass transport, a Dirichlet boundary conditions with concentration $c = 0$ is set at the outer shell. The inner boundary condition is equivalent to the eighth of a total abstraction rate of $Q_t = 15 m^3/d$ for a full cylinder. *NB: In the `ComponentTransport` process, the Neumann BC is given as mass flux and has to be calculated per area, such that the value for the project file is $Q = Q_t / 8 / A \cdot \rho = 2.83542E-03 m^3/s/m^2 \cdot kg/m^3$ with fluid density $\rho = 1000 kg/m^3$ and abstraction area $A = 7.65 m^2$.* + + +The homogeneous, isotropic domain is defined for the radius $1 < r < 100 m$ and a thickness $b = 10 m$. Saturated intrinsic permeability is $\kappa = 7.6453E-13 m^2$ yielding a transmissivity of $T = 7.5E-05 m^2/s$; porosity is $\phi = 0.2$; specific storage is $S_s = 1.0E-03$ and defined through compressibility $\gamma = 5.0968E-08 s^2/m/kg$ (input tag fluid_density_pressure_difference_ratio is $\frac{\partial \rho}{\partial p} = \frac{S_s}{b \phi g \rho}$ with gravitational acceleration $g = 9.81 m^2/s$). + +Mass transport properties are irrelevant as no transport processes are calculated. + +Initial conditions are $c = 0$ and hydrostatic pressure conditions. + +{{< data-link "Link to the HC_theis project file" "Parabolic/ComponentTransport/HC_Theis/HC_theis.prj" >}} + + +### Results + +The figure below compares the analytical Theis solution vs. the simulated values from OGS6. + +{{< img src="../comparison.png" title="Comparison between numerical (crosses) and analytical (lines) values.">}} + +The top figure shows drawdown (i.e. the difference in water level compared to an initial state) over time at distance $r = 30 m$: for a simulation time $t < 40000 s$, the differences between analytical and numerical solutions are marginal; at later simulation times, the drawdown shows lower values than predicted from the analytical solution, as it is influenced by the outer Dirichlet pressure boundary condition. + +The lower figure shows drawdown over radius at time $t = 5000 s$; the top figure also signifies this with a green vertical: over the whole domain, the analytical and numerical solutions are coinciding very well. *NB: With higher values of $S_s$, one has to take care to convert the simulated water level to equivalent freshwater head; in this case, fluid density variation is very low such that a conversion is not required.* + + +## References + +Theis, C.V., 1935. The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage. Trans. Amer. Geophys. Union 16, 513–514. + +Walther, M., 2014. Variable-Density Flow Processes in Porous Media On Small, Medium and Regional Scales (Dissertation). Technische Universität Dresden. diff --git a/web/content/docs/benchmarks/hydro-component/theis/comparison.png b/web/content/docs/benchmarks/hydro-component/theis/comparison.png new file mode 100644 index 00000000000..19a12772360 --- /dev/null +++ b/web/content/docs/benchmarks/hydro-component/theis/comparison.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f846c43166cbf6379948690261b67f48d6fc44d8082181b2e08f3ff9a3dbeba9 +size 38126 -- GitLab