From 9452965ef4fb751b20b6016071a972c4e125d7ab Mon Sep 17 00:00:00 2001
From: HBShaoUFZ <36633245+HBShaoUFZ@users.noreply.github.com>
Date: Wed, 7 Mar 2018 17:16:45 +0100
Subject: [PATCH] [Web] Add the benchmark "Buildup Test" (#2089)
* add the content of the benchmark buildup test
* add the benchmark description.
* remove tailing white space.
* fix the table format.
* fix figures
* linking the figures
* add input files to the Test data
* move input files to the LFS
* minor language and format issues fixed
* add standard benchmark results.
* activate the test
* correct the file name.
* fixing two issues raised by WW.
1) Fixing typo in the benchmark document;
2) Only print out the necessary time step for comparison.
---
ProcessLib/LiquidFlow/Tests.cmake | 12 +
.../LiquidFlow/BuildupTest/buildup_test.prj | 270 ++++++++++++++++++
.../LiquidFlow/BuildupTest/line_1000_axi.gml | 3 +
.../LiquidFlow/BuildupTest/line_1000_axi.vtu | 3 +
...ldup_test_pcs_0_ts_107_t_424800.000000.vtu | 3 +
...ldup_test_pcs_0_ts_211_t_720000.000000.vtu | 3 +
.../liquid-flow/buildup_test.pandoc | 150 ++++++++++
.../benchmarks/liquid-flow/comparison.png | 3 +
.../docs/benchmarks/liquid-flow/error.png | 3 +
.../docs/benchmarks/liquid-flow/horner.png | 3 +
10 files changed, 453 insertions(+)
create mode 100644 Tests/Data/Parabolic/LiquidFlow/BuildupTest/buildup_test.prj
create mode 100644 Tests/Data/Parabolic/LiquidFlow/BuildupTest/line_1000_axi.gml
create mode 100644 Tests/Data/Parabolic/LiquidFlow/BuildupTest/line_1000_axi.vtu
create mode 100644 Tests/Data/Parabolic/LiquidFlow/BuildupTest/standard_solution_buildup_test_pcs_0_ts_107_t_424800.000000.vtu
create mode 100644 Tests/Data/Parabolic/LiquidFlow/BuildupTest/standard_solution_buildup_test_pcs_0_ts_211_t_720000.000000.vtu
create mode 100644 web/content/docs/benchmarks/liquid-flow/buildup_test.pandoc
create mode 100644 web/content/docs/benchmarks/liquid-flow/comparison.png
create mode 100644 web/content/docs/benchmarks/liquid-flow/error.png
create mode 100644 web/content/docs/benchmarks/liquid-flow/horner.png
diff --git a/ProcessLib/LiquidFlow/Tests.cmake b/ProcessLib/LiquidFlow/Tests.cmake
index dafcce389bb..3a092a9f04c 100644
--- a/ProcessLib/LiquidFlow/Tests.cmake
+++ b/ProcessLib/LiquidFlow/Tests.cmake
@@ -45,6 +45,18 @@ AddTest(
DIFF_DATA
axisym_theis.vtu liquid_pcs_pcs_0_ts_30_t_1728.000000.vtu OGS5_pressure pressure 1e-8 1e-8
)
+AddTest(
+ NAME LiquidFlow_BuildupTest
+ PATH Parabolic/LiquidFlow/BuildupTest
+ EXECUTABLE ogs
+ EXECUTABLE_ARGS buildup_test.prj
+ WRAPPER time
+ TESTER vtkdiff
+ REQUIREMENTS NOT OGS_USE_MPI
+ DIFF_DATA
+ standard_solution_buildup_test_pcs_0_ts_107_t_424800.000000.vtu buildup_test_pcs_0_ts_107_t_424800.000000.vtu pressure pressure 1e-12 0.0
+ standard_solution_buildup_test_pcs_0_ts_211_t_720000.000000.vtu buildup_test_pcs_0_ts_211_t_720000.000000.vtu pressure pressure 1e-12 0.0
+)
AddTest(
NAME LARGE_LiquidFlow_Anisotropic_GravityDriven3D
diff --git a/Tests/Data/Parabolic/LiquidFlow/BuildupTest/buildup_test.prj b/Tests/Data/Parabolic/LiquidFlow/BuildupTest/buildup_test.prj
new file mode 100644
index 00000000000..d9385c546aa
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/BuildupTest/buildup_test.prj
@@ -0,0 +1,270 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+ <mesh axially_symmetric="true">line_1000_axi.vtu</mesh>
+ <geometry>line_1000_axi.gml</geometry>
+ <processes>
+ <process>
+ <name>LiquidFlow</name>
+ <type>LIQUID_FLOW</type>
+ <integration_order>2</integration_order>
+ <darcy_gravity>
+ <!-- axis_id: 0, 1, or the dimension of space minus one -->
+ <axis_id>1</axis_id>
+ <!-- g>=0. g=0: non gravity term -->
+ <g>0.</g>
+ </darcy_gravity>
+ <process_variables>
+ <process_variable>pressure</process_variable>
+ </process_variables>
+ <secondary_variables>
+ <secondary_variable type="static" internal_name="darcy_velocity" output_name="v"/>
+ </secondary_variables>
+ <material_property>
+ <fluid>
+ <density>
+ <type>Constant</type>
+ <value> 78.68 </value>
+ </density>
+ <viscosity>
+ <type>Constant</type>
+ <value> 1.295e-4 </value>
+ </viscosity>
+ </fluid>
+ <porous_medium>
+ <porous_medium id="0">
+ <permeability>
+ <permeability_tensor_entries>kappa1</permeability_tensor_entries>
+ <type>Constant</type>
+ </permeability>
+ <porosity>
+ <type>Constant</type>
+ <porosity_parameter>constant_porosity_parameter</porosity_parameter>
+ </porosity>
+ <storage>
+ <type>Constant</type>
+ <value> 8.05e-7 </value>
+ </storage>
+ </porous_medium>
+ </porous_medium>
+ </material_property>
+ </process>
+ </processes>
+ <time_loop>
+ <processes>
+ <process ref="LiquidFlow">
+ <nonlinear_solver>basic_picard</nonlinear_solver>
+ <convergence_criterion>
+ <type>DeltaX</type>
+ <norm_type>NORM2</norm_type>
+ <abstol>1.e-6</abstol>
+ </convergence_criterion>
+ <time_discretization>
+ <type>BackwardEuler</type>
+ </time_discretization>
+ <output>
+ <variables>
+ <variable> pressure </variable>
+ <variable> v </variable>
+ </variables>
+ </output>
+ <time_stepping>
+ <type>FixedTimeStepping</type>
+ <t_initial> 0.0 </t_initial>
+ <t_end> 720000 </t_end>
+ <timesteps>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>0.432</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>0.864</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>4.32</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>8.64</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>43.2</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>86.4</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>432.0</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>864.0</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>4320.</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>8640.</delta_t>
+ </pair>
+ <pair>
+ <repeat>6</repeat>
+ <delta_t>43200.</delta_t>
+ </pair>
+ <pair>
+ <repeat>1</repeat>
+ <delta_t>21601.44</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>0.432</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>0.864</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>4.32</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>8.64</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>43.2</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>86.4</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>432.0</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>864.0</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>4320.</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>8640.</delta_t>
+ </pair>
+ <pair>
+ <repeat>10</repeat>
+ <delta_t>43200.</delta_t>
+ </pair>
+ </timesteps>
+ </time_stepping>
+ </process>
+ </processes>
+ <output>
+ <type>VTK</type>
+ <prefix>buildup_test</prefix>
+ <timesteps>
+ <pair>
+ <repeat> 1 </repeat>
+ <each_steps> 107 </each_steps>
+ </pair>
+ </timesteps>
+ </output>
+ </time_loop>
+ <parameters>
+ <parameter>
+ <name>p0</name>
+ <type>Constant</type>
+ <value>67.5e5</value>
+ </parameter>
+ <parameter>
+ <name>p_dbc</name>
+ <type>Constant</type>
+ <value>67.5e5</value>
+ </parameter>
+ <parameter>
+ <name>constant_porosity_parameter</name>
+ <type>Constant</type>
+ <value>1</value>
+ </parameter>
+ <parameter>
+ <name>kappa1</name>
+ <type>Constant</type>
+ <values>9.2e-12</values>
+ </parameter>
+ <parameter>
+ <name>p_spatial</name>
+ <type>Constant</type>
+ <value>1</value>
+ </parameter>
+ <parameter>
+ <name>pressure_source_term</name>
+ <type>CurveScaled</type>
+ <curve>pressure_source_term_temporal</curve>
+ <parameter>p_spatial</parameter>
+ </parameter>
+ </parameters>
+ <curves>
+ <curve>
+ <name>pressure_source_term_temporal</name>
+ <coords> 0 424800 424800.001 849600</coords>
+ <values> -0.2754 -0.2754 0 0</values>
+ </curve>
+ </curves>
+ <process_variables>
+ <process_variable>
+ <name>pressure</name>
+ <components>1</components>
+ <order>1</order>
+ <initial_condition>p0</initial_condition>
+ <boundary_conditions>
+ <boundary_condition>
+ <geometrical_set>geometry</geometrical_set>
+ <geometry>outer</geometry>
+ <type>Dirichlet</type>
+ <parameter>p_dbc</parameter>
+ </boundary_condition>
+ </boundary_conditions>
+ <source_terms>
+ <source_term>
+ <geometrical_set>geometry</geometrical_set>
+ <geometry>inner</geometry>
+ <type>Nodal</type>
+ <parameter>pressure_source_term</parameter>
+ </source_term>
+ </source_terms>
+ </process_variable>
+ </process_variables>
+ <nonlinear_solvers>
+ <nonlinear_solver>
+ <name>basic_picard</name>
+ <type>Picard</type>
+ <max_iter>10</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-20 -maxiter 10000</lis>
+ <eigen>
+ <solver_type>CG</solver_type>
+ <precon_type>DIAGONAL</precon_type>
+ <max_iteration_step>10000</max_iteration_step>
+ <error_tolerance>1e-20</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/LiquidFlow/BuildupTest/line_1000_axi.gml b/Tests/Data/Parabolic/LiquidFlow/BuildupTest/line_1000_axi.gml
new file mode 100644
index 00000000000..29869a1e62c
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/BuildupTest/line_1000_axi.gml
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6e1ce78c91d3ad568e0f3b530da064658a3c48da4331d182ee7f880c17a34eba
+size 483
diff --git a/Tests/Data/Parabolic/LiquidFlow/BuildupTest/line_1000_axi.vtu b/Tests/Data/Parabolic/LiquidFlow/BuildupTest/line_1000_axi.vtu
new file mode 100644
index 00000000000..06110f1294a
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/BuildupTest/line_1000_axi.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a9bd6cad0e07b339a979478ba26bb5b6d0bc9e9aa405b10ea1be65405770b93f
+size 71753
diff --git a/Tests/Data/Parabolic/LiquidFlow/BuildupTest/standard_solution_buildup_test_pcs_0_ts_107_t_424800.000000.vtu b/Tests/Data/Parabolic/LiquidFlow/BuildupTest/standard_solution_buildup_test_pcs_0_ts_107_t_424800.000000.vtu
new file mode 100644
index 00000000000..6b37784d92e
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/BuildupTest/standard_solution_buildup_test_pcs_0_ts_107_t_424800.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4bf448b0b3e36195d5c06aebb7b95bfd643dd90414a952aa1d774e77c2100a61
+size 35759
diff --git a/Tests/Data/Parabolic/LiquidFlow/BuildupTest/standard_solution_buildup_test_pcs_0_ts_211_t_720000.000000.vtu b/Tests/Data/Parabolic/LiquidFlow/BuildupTest/standard_solution_buildup_test_pcs_0_ts_211_t_720000.000000.vtu
new file mode 100644
index 00000000000..4914b639bce
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/BuildupTest/standard_solution_buildup_test_pcs_0_ts_211_t_720000.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d00ca55fa12f71153abb5e2d6a0159b528eda98f3219d7cd2edcbc9309191b15
+size 26606
diff --git a/web/content/docs/benchmarks/liquid-flow/buildup_test.pandoc b/web/content/docs/benchmarks/liquid-flow/buildup_test.pandoc
new file mode 100644
index 00000000000..939e41e51f4
--- /dev/null
+++ b/web/content/docs/benchmarks/liquid-flow/buildup_test.pandoc
@@ -0,0 +1,150 @@
++++
+author = "Boyan Meng and Haibing Shao"
+date = "2018-02-27T16:44:00+01:00"
+title = "Buildup Test"
+weight = 172
+project = "/Parabolic/LiquidFlow/BuildupTest/buildup_test.prj"
+
+[menu]
+ [menu.benchmarks]
+ parent = "liquid-flow"
+
++++
+
+{{< data-link >}}
+
+Problem description {#problem-description .unnumbered .unnumbered}
+===================
+
+The pressure buildup test is performed by shutting in a producing well
+at time $t=t_p$, after which a smooth rise of the well head pressure can
+be observed. For a geothermal reservoir, the buildup test result is
+interpreted using a Horner plot in order to evaluate the reservoir
+permeability or transmissivity. In this benchmark, observation data from
+a geothermal well is employed to parameterize the numerical model. In
+the model, a time dependent nodal source term was set up to represent
+the shut-in operation. The simulated pressure profile is then verified
+against the analytical solution.
+
+Model Setup {#model-setup .unnumbered .unnumbered}
+===========
+
+This benchmark represents a scenario in which the well had been
+producing geothermal brine for $118\ \mathrm{h}$ at a rate of
+$78\ t/\mathrm{h}$ and was then shut in for a buildup test. At the given
+reservoir temperature (260$^\circ$C) and pressure ($47\ \mathrm{bar}$), the
+density and viscosity of the water and steam mixture were calculated as
+$\rho=78.68\ \mathrm{kg/m^3}$ and
+$\mu=1.295\times10^{-4}\ \mathrm{Pa\ s}$. The compressibility of the
+mixture was estimated as $nc_t=0.0805\ \mathrm{bar^{-1}}$ ($n$ refers to
+the porosity of the reservoir), which yields a specific storage
+coefficient of $S=\rho gnc_t=6.21\times 10^{-4}\ \mathrm{m^{-1}}$. The
+observed pressure readings during the buildup test are cited from
+Chapter 6 of the book *Geothermal Power Generation*
+[1], and the data is archived in the Appendix.
+
+The permeability of the reservoir can be estimated by means of a Horner
+plot, in which the pressure $p$ is plotted against
+$(t_p+\Delta t)/\Delta t$, i.e. Horner time on a semi-logarithmic scale
+(cf. Figure 1). In the Horner plot, the data points form a
+straight line in the late-time period of the test. Note that the time
+increases in the opposite direction of the *X*-axis. Therefore, the
+linear section appears at the left side of the diagram.
+
+\centering
+{{< img src="../horner.png" >}}
+
+Figure 1: Horner plot ($p$ vs $(t_p+\Delta t)/\Delta t$) for buildup test showing the inferred Horner straight line
+
+
+The slope $m$ of the Horner straight line is expressed as:
+$$m=0.1832\frac{Q\mu}{\kappa b}$$ in which $Q\ \mathrm{[L^3/T]}\ (Q>0)$
+is the production rate of the well before shut-in,
+$\kappa\ \mathrm{[L^2]}$ is the permeability and $b\ \mathrm{[L]}$ is
+the aquifer thickness. From the Horner plot, we can infer a Horner
+straight line with a slope of $m=0.79$. Therefore the transmissivity of
+the aquifer can be calculated as $$\begin{aligned}
+\kappa b&=&0.1832\frac{Q\mu}{m}=0.1832\frac{((78000/3600)/78.68)\times1.295\times10^{-4}}{7.09\times10^5}\\&=&9.2\times10^{-12}\ \mathrm{m^3}\end{aligned}$$
+In addition, the straight line in the Horner plot can be extracted to a Horner time of 1,
+which corresponds to the infinite shut-in time $(\Delta t)$. This leads to
+an extrapolated pressure $p_0$ of $67.5~\mathrm{kPa}$, which is the
+undisturbed reservoir pressure .
+
+Input files {#input-files .unnumbered .unnumbered}
+===========
+
+The benchmark project is defined in the input file 'buildup\_test.prj'. It defines the process to
+be solved as "LiquidFlow" and the primary variable is hence pressure.
+The initial condition is set to $p_0=67.5\ \mathrm{bar}$ and the
+undisturbed boundary is achieved by a large domain size
+$(r=1000\ \mathrm{m})$. The time-dependent source term is applied in this
+benchmark. From the beginning until $t=424800$ sec, the pumping rate was
+maintained at a constant rate. Afterwards, the well is shut-in and pressure
+starts to build up. The geometries used to specify the model domain, boundary
+conditions, and source term can be found in 'line\_1000\_axi.gml' file.
+The mesh is specified in 'line\_1000\_axi.vtu', which is stored in the
+VTK format and can be directly visualized in Paraview.
+
+Analytical solution {#analytical-solution .unnumbered .unnumbered}
+===================
+
+The pressure buildup test is comparable to a pumping recovery test as
+the extraction rate is first kept constant at $Q$, and then becomes zero
+at $t=t_p$. This benchmark then adopts the same assumptions as in the
+[Theis'
+problem](https://benchmarks.opengeosys.org/docs/benchmarks/liquid-flow/liquid-flow-theis-problem/).
+The analytical solution of the pressure difference $\Delta p$ with
+respect to the initial pressure $p_0$ is the sum of two Theis curves:
+one starting at $t=0$ and another starting at $t=t_p$ but with an
+opposite extraction rate, i.e. for $t\leq t_p$,
+$$\Delta p=\rho g \frac{-Q}{4\pi T}W\left(\frac{r^2S}{4Tt}\right)$$ and
+for $t>t_p$,
+$$\Delta p=\rho g \frac{-Q}{4\pi T}W\left(\frac{r^2S}{4Tt}\right)+\rho g \frac{Q}{4\pi T}W\left(\frac{r^2S}{4T(t-t_p)}\right)$$
+
+Results and evaluation {#results-and-evaluation .unnumbered .unnumbered}
+======================
+
+The pressure evolution is simulated throughout the domain and the result
+is compared with the analytical solution at $r=10.287\ \mathrm{m}$. In
+Figure 2, it can be observed that the numerical model
+fits with the analytical solution very well. The absolute and relative
+error between the analytical and numerical solution is depicted in
+Figure 3.
+
+{{< img src="../comparison.png" >}}
+
+
+Figure 2: OGS 6 result compared with analytical solution
+
+{{< img src="../error.png" >}}
+
+
+Figure 3: Absolute and relative error
+
+References {#references .unnumbered .unnumbered}
+========
+[1] RN Horne. Characterization, evaluation, and interpretation of well data. In: R DiPippo, editor,Geothermal Power Generation, chapter 6, pages 141–163.Elsevier, 2016.
+
+Appendix {#appendix .unnumbered .unnumbered}
+========
+
+\centering
+| $\Delta t$ (h) | $\Delta p$ (bar) | $\Delta t$ (h) | $\Delta p$ (bar) |
+| :------------: |:-----------------: | :---------------:| :---------------:|
+| 0.0024 | 0.174 | 0.1708 | 3.65 |
+| 0.0073 | 0.695 | 0.2442 | 4.00 |
+| 0.0098 | 1.13 | 0.3667 | 4.26 |
+| 0.0122 | 1.30 | 0.6111 | 5.13 |
+| 0.0171 | 1.57 | 0.8556 | 6.35 |
+| 0.022 | 1.74 | 1.2194 | 7.48 |
+| 0.0244 | 1.91 | 1.5861 | 8.17 |
+| 0.0292 | 2.00 | 1.8361 | 8.43 |
+| 0.0367 | 2.09 | 2.4417 | 9.22 |
+| 0.0414 | 2.17 | 3.4167 | 10.2 |
+| 0.0489 | 2.43 | 3.8611 | 10.4 |
+| 0.0586 | 2.61 | 6.3056 | 11.8 |
+| 0.0733 | 2.78 | 8.3056 | 12.6 |
+| 0.0856 | 2.96 | 10.9722 | 13.2 |
+| 0.0975 | 3.13 | | |
+
+ : Pressure measurements during well buildup[]{label="table:1"}
diff --git a/web/content/docs/benchmarks/liquid-flow/comparison.png b/web/content/docs/benchmarks/liquid-flow/comparison.png
new file mode 100644
index 00000000000..8b693f33e9d
--- /dev/null
+++ b/web/content/docs/benchmarks/liquid-flow/comparison.png
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+version https://git-lfs.github.com/spec/v1
+oid sha256:ed8108d7ce33916d5ff0db71d303f867342a9a9128d232636ef0f6392455c9f9
+size 4457
diff --git a/web/content/docs/benchmarks/liquid-flow/error.png b/web/content/docs/benchmarks/liquid-flow/error.png
new file mode 100644
index 00000000000..8cb06288d52
--- /dev/null
+++ b/web/content/docs/benchmarks/liquid-flow/error.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4a4c4ed3bc4132f8ac6061e164be8826e26f950223d486e541bcca69748b80ae
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diff --git a/web/content/docs/benchmarks/liquid-flow/horner.png b/web/content/docs/benchmarks/liquid-flow/horner.png
new file mode 100644
index 00000000000..dd015c20f24
--- /dev/null
+++ b/web/content/docs/benchmarks/liquid-flow/horner.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:50a3bb0be03d659f0c93536fde1b29c92d90410a559bc3a8794ab970f8f5c7ea
+size 11774
--
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