diff --git a/dumux/freeflow/rans/vtkoutputfields.hh b/dumux/freeflow/rans/vtkoutputfields.hh
index 631bb23006bb565e834c90c69ef3e0e34a25e26b..ff84b83d83c4fcfe5419847d2bd3d3dc477b94da 100644
--- a/dumux/freeflow/rans/vtkoutputfields.hh
+++ b/dumux/freeflow/rans/vtkoutputfields.hh
@@ -24,10 +24,7 @@
#ifndef DUMUX_RANS_VTK_OUTPUT_FIELDS_HH
#define DUMUX_RANS_VTK_OUTPUT_FIELDS_HH
-#include <dune/common/fvector.hh>
-#include <dumux/common/properties.hh>
-#include <dumux/common/parameters.hh>
-#include <dumux/discretization/methods.hh>
+#include <dumux/freeflow/navierstokes/vtkoutputfields.hh>
namespace Dumux
{
@@ -37,59 +34,29 @@ namespace Dumux
* \brief Adds vtk output fields for the Reynolds-Averaged Navier-Stokes model
*/
template<class FVGridGeometry>
-class RANSVtkOutputFields
+class RANSVtkOutputFields : public NavierStokesVtkOutputFields<FVGridGeometry>
{
- using ctype = typename FVGridGeometry::GridView::ctype;
- using GlobalPosition = Dune::FieldVector<ctype, FVGridGeometry::GridView::dimensionworld>;
-
- // Helper type used for tag dispatching (to add discretization-specific fields).
- template<DiscretizationMethod discMethod>
- using discMethodTag = std::integral_constant<DiscretizationMethod, discMethod>;
+ enum { dim = FVGridGeometry::GridView::dimension };
public:
//! Initialize the Navier-Stokes specific vtk output fields.
template <class VtkOutputModule>
static void init(VtkOutputModule& vtk)
{
- vtk.addVolumeVariable([](const auto& v){ return v.velocity()[0]; }, "v_x [m/s]");
- vtk.addVolumeVariable([](const auto& v){ return v.velocityGradients()[0][0]; }, "dv_x/dx [m/s]");
- vtk.addVolumeVariable([](const auto& v){ return v.velocityGradients()[0][1]; }, "dv_x/dy [m/s]");
- vtk.addVolumeVariable([](const auto& v){ return v.pressure(); }, "p [Pa]");
- vtk.addVolumeVariable([](const auto& v){ return v.pressure() - 1e5; }, "p_rel [Pa]");
- vtk.addVolumeVariable([](const auto& v){ return v.density(); }, "rho [kg/m^3]");
- vtk.addVolumeVariable([](const auto& v){ return v.viscosity() / v.density(); }, "nu [m^2/s]");
- vtk.addVolumeVariable([](const auto& v){ return v.dynamicEddyViscosity() / v.density(); }, "nu_t [m^2/s]");
- vtk.addVolumeVariable([](const auto& v){ return v.wallDistance(); }, "l_w [m]");
- vtk.addVolumeVariable([](const auto& v){ return v.yPlus(); }, "y^+ [-]");
- vtk.addVolumeVariable([](const auto& v){ return v.uPlus(); }, "u^+ [-]");
-
- // add discretization-specific fields
- additionalOutput_(vtk, discMethodTag<FVGridGeometry::discMethod>{});
- }
-
-private:
-
- //! Adds discretization-specific fields (nothing by default).
- template <class VtkOutputModule, class AnyMethod>
- static void additionalOutput_(VtkOutputModule& vtk, AnyMethod)
- { }
-
- //! Adds discretization-specific fields (velocity vectors on the faces for the staggered discretization).
- template <class VtkOutputModule>
- static void additionalOutput_(VtkOutputModule& vtk, discMethodTag<DiscretizationMethod::staggered>)
- {
- const bool writeFaceVars = getParamFromGroup<bool>(vtk.paramGroup(), "Vtk.WriteFaceData", false);
- if(writeFaceVars)
- {
- auto faceVelocityVector = [](const typename FVGridGeometry::SubControlVolumeFace& scvf, const auto& faceVars)
- {
- GlobalPosition velocity(0.0);
- velocity[scvf.directionIndex()] = faceVars.velocitySelf();
- return velocity;
- };
+ NavierStokesVtkOutputFields<FVGridGeometry>::init(vtk);
- vtk.addFaceVariable(faceVelocityVector, "faceVelocity");
- }
+ vtk.addVolumeVariable([](const auto& v){ return v.velocityGradients()[0]; }, "dv_x/dx_");
+ if (dim > 1)
+ vtk.addVolumeVariable([](const auto& v){ return v.velocityGradients()[1]; }, "dv_y/dx_");
+ if (dim > 2)
+ vtk.addVolumeVariable([](const auto& v){ return v.velocityGradients()[2]; }, "dv_z/dx_");
+ vtk.addVolumeVariable([](const auto& v){ return v.pressure() - 1e5; }, "p_rel");
+ vtk.addVolumeVariable([](const auto& v){ return v.density(); }, "rho");
+ vtk.addVolumeVariable([](const auto& v){ return v.viscosity() / v.density(); }, "nu");
+ vtk.addVolumeVariable([](const auto& v){ return v.dynamicEddyViscosity() / v.density(); }, "nu_t");
+ vtk.addVolumeVariable([](const auto& v){ return v.wallDistance(); }, "l_w");
+ vtk.addVolumeVariable([](const auto& v){ return v.yPlus(); }, "y^+");
+ vtk.addVolumeVariable([](const auto& v){ return v.uPlus(); }, "u^+");
}
};
diff --git a/dumux/io/vtkoutputmodule.hh b/dumux/io/vtkoutputmodule.hh
index 55f715fd5a1b111d49aa2b4e396188c3f4301e4b..e3c8177b9d31e08542e836c91362235678d2e109 100644
--- a/dumux/io/vtkoutputmodule.hh
+++ b/dumux/io/vtkoutputmodule.hh
@@ -239,6 +239,7 @@ class VtkOutputModule
static constexpr int dofCodim = isBox ? dim : 0;
struct VolVarScalarDataInfo { std::function<Scalar(const VolumeVariables&)> get; std::string name; };
+ struct VolVarVectorDataInfo { std::function<GlobalPosition(const VolumeVariables&)> get; std::string name; };
using Field = Vtk::template Field<GridView>;
public:
@@ -293,6 +294,16 @@ public:
volVarScalarDataInfo_.push_back(VolVarScalarDataInfo{f, name});
}
+ //! Add a vector-valued variable
+ //! \param f A function taking a VolumeVariables object and returning the desired vector
+ //! \param name The name of the vtk field
+ //! \note This method is only available for dimWorld > 1. For 1-D problems, the overload for volVar methods returning a Scalar will be used.
+ template<class G = GlobalPosition, typename std::enable_if_t<(G::dimension > 1), int> = 0>
+ void addVolumeVariable(std::function<GlobalPosition(const VolumeVariables&)>&& f, const std::string& name)
+ {
+ volVarVectorDataInfo_.push_back(VolVarVectorDataInfo{f, name});
+ }
+
//! Add a scalar or vector valued vtk field
//! \param v The field to be added. Can be any indexable container. Its value type can be a number or itself an indexable container.
//! \param name The name of the field
@@ -367,9 +378,11 @@ public:
// volume variable data
std::vector<std::vector<Scalar>> volVarScalarData;
+ std::vector<std::vector<GlobalPosition>> volVarVectorData;
//! Abort if no data was registered
if (!volVarScalarDataInfo_.empty()
+ || !volVarVectorDataInfo_.empty()
|| !fields_.empty()
|| velocityOutput.enableOutput()
|| addProcessRank)
@@ -380,6 +393,8 @@ public:
// get fields for all volume variables
if (!volVarScalarDataInfo_.empty())
volVarScalarData.resize(volVarScalarDataInfo_.size(), std::vector<Scalar>(numDofs));
+ if (!volVarVectorDataInfo_.empty())
+ volVarVectorData.resize(volVarVectorDataInfo_.size(), std::vector<GlobalPosition>(numDofs));
if (velocityOutput.enableOutput())
{
@@ -416,15 +431,21 @@ public:
else if (!volVarScalarDataInfo_.empty())
elemVolVars.bindElement(element, fvGeometry, sol_);
- if (!volVarScalarDataInfo_.empty())
+ if (!volVarScalarDataInfo_.empty()
+ || !volVarVectorDataInfo_.empty())
{
for (auto&& scv : scvs(fvGeometry))
{
const auto dofIdxGlobal = scv.dofIndex();
const auto& volVars = elemVolVars[scv];
+ // get the scalar-valued data
for (std::size_t i = 0; i < volVarScalarDataInfo_.size(); ++i)
volVarScalarData[i][dofIdxGlobal] = volVarScalarDataInfo_[i].get(volVars);
+
+ // get the vector-valued data
+ for (std::size_t i = 0; i < volVarVectorDataInfo_.size(); ++i)
+ volVarVectorData[i][dofIdxGlobal] = volVarVectorDataInfo_[i].get(volVars);
}
}
@@ -445,6 +466,12 @@ public:
// volume variables if any
for (std::size_t i = 0; i < volVarScalarDataInfo_.size(); ++i)
addDofDataForWriter_(sequenceWriter_, volVarScalarData[i], volVarScalarDataInfo_[i].name);
+ for (std::size_t i = 0; i < volVarVectorDataInfo_.size(); ++i)
+ {
+
+ sequenceWriter_.addCellData(Field(gridGeom_.gridView(), gridGeom_.elementMapper(), volVarVectorData[i],
+ volVarVectorDataInfo_[i].name, dimWorld, 0).get());
+ }
// the velocity field
if (velocityOutput.enableOutput())
@@ -551,7 +578,9 @@ private:
std::shared_ptr<Dune::VTKWriter<GridView>> writer_;
Dune::VTKSequenceWriter<GridView> sequenceWriter_;
- std::vector<VolVarScalarDataInfo> volVarScalarDataInfo_; //!< Registered volume variables
+ std::vector<VolVarScalarDataInfo> volVarScalarDataInfo_; //!< Registered volume variables (scalar)
+ std::vector<VolVarVectorDataInfo> volVarVectorDataInfo_; //!< Registered volume variables (vector)
+
std::vector<Field> fields_; //!< Registered scalar and vector fields
};
diff --git a/dumux/porousmediumflow/mpnc/vtkoutputfields.hh b/dumux/porousmediumflow/mpnc/vtkoutputfields.hh
index 03e28c84e9c2d2b8e89e3c0163d60fd95f0797f7..415a371a628e3912ae596d22ba69f93983d62ef3 100644
--- a/dumux/porousmediumflow/mpnc/vtkoutputfields.hh
+++ b/dumux/porousmediumflow/mpnc/vtkoutputfields.hh
@@ -43,14 +43,14 @@ public:
for (int i = 0; i < FluidSystem::numPhases; ++i)
vtk.addVolumeVariable([i](const auto& v){ return v.saturation(i); }, "S_"+ FluidSystem::phaseName(i));
- for (int i = 0; i < FluidSystem::numPhases; ++i)
+ for (int i = 0; i < FluidSystem::numPhases; ++i)
vtk.addVolumeVariable([i](const auto& v){ return v.pressure(i); }, "p_"+ FluidSystem::phaseName(i));
- for (int i = 0; i < FluidSystem::numPhases; ++i)
+ for (int i = 0; i < FluidSystem::numPhases; ++i)
vtk.addVolumeVariable([i](const auto& v){ return v.density(i); }, "rho_"+ FluidSystem::phaseName(i));
- for (int i = 0; i < FluidSystem::numPhases; ++i)
- vtk.addVolumeVariable([i](const auto& v){ return v.mobility(i); },"lambda_"+ FluidSystem::phaseName(i));
+ for (int i = 0; i < FluidSystem::numPhases; ++i)
+ vtk.addVolumeVariable([i](const auto& v){ return v.mobility(i); },"lambda_"+ FluidSystem::phaseName(i));
vtk.addVolumeVariable([](const auto& v){ return v.porosity(); }, "porosity");
diff --git a/dumux/porousmediumflow/nonequilibrium/vtkoutputfields.hh b/dumux/porousmediumflow/nonequilibrium/vtkoutputfields.hh
index 62253bad4bc4631bf613adbbd9160a8c4be324c2..6d5652a9e2d57a57002b022a2f4b7bde076f4ed5 100644
--- a/dumux/porousmediumflow/nonequilibrium/vtkoutputfields.hh
+++ b/dumux/porousmediumflow/nonequilibrium/vtkoutputfields.hh
@@ -42,14 +42,14 @@ public:
static void init(VtkOutputModule& vtk)
{
EquilibriumVtkOutputFields::init(vtk);
- for (int i = 0; i < numEnergyEqFluid; ++i)
- vtk.addVolumeVariable( [i](const auto& v){ return v.temperature(i); }, "T_" + FluidSystem::phaseName(i) );
- for (int i = 0; i < numEnergyEqSolid; ++i)
- vtk.addVolumeVariable( [i](const auto& v){ return v.temperatureSolid(); }, "T_solid" );
+ for (int i = 0; i < numEnergyEqFluid; ++i)
+ vtk.addVolumeVariable( [i](const auto& v){ return v.temperature(i); }, "T_" + FluidSystem::phaseName(i) );
+ for (int i = 0; i < numEnergyEqSolid; ++i)
+ vtk.addVolumeVariable( [i](const auto& v){ return v.temperatureSolid(); }, "T_solid" );
for (int i = 0; i < FluidSystem::numPhases; ++i){
- vtk.addVolumeVariable( [i](const auto& v){ return v.reynoldsNumber(i); }, "reynoldsNumber_" + FluidSystem::phaseName(i) );
- vtk.addVolumeVariable( [i](const auto& v){ return v.nusseltNumber(i); }, "nusseltNumber_" + FluidSystem::phaseName(i) );
- vtk.addVolumeVariable( [i](const auto& v){ return v.prandtlNumber(i); }, "prandtlNumber_" + FluidSystem::phaseName(i) );
+ vtk.addVolumeVariable( [i](const auto& v){ return v.reynoldsNumber(i); }, "reynoldsNumber_" + FluidSystem::phaseName(i) );
+ vtk.addVolumeVariable( [i](const auto& v){ return v.nusseltNumber(i); }, "nusseltNumber_" + FluidSystem::phaseName(i) );
+ vtk.addVolumeVariable( [i](const auto& v){ return v.prandtlNumber(i); }, "prandtlNumber_" + FluidSystem::phaseName(i) );
}
}
};
diff --git a/dumux/porousmediumflow/richards/vtkoutputfields.hh b/dumux/porousmediumflow/richards/vtkoutputfields.hh
index b0b1ee249695a1597b03b9c21ad935845e85e12a..3506564e988a7286763ccb5f2ec1ec7e4228e993 100644
--- a/dumux/porousmediumflow/richards/vtkoutputfields.hh
+++ b/dumux/porousmediumflow/richards/vtkoutputfields.hh
@@ -59,8 +59,7 @@ public:
vtk.addVolumeVariable([](const auto& v){ return v.moleFraction(1, 0); }, "x^w_air");
vtk.addVolumeVariable([](const auto& v){ return v.waterContent(Indices::wPhaseIdx); },"water content");
- vtk.addVolumeVariable([](const auto& v){ return v.priVars().state(); }, "phasePresence");
-
+ vtk.addVolumeVariable([](const auto& v){ return v.priVars().state(); }, "phasePresence");
}
};
diff --git a/test/freeflow/rans/test_pipe_laufer.cc b/test/freeflow/rans/test_pipe_laufer.cc
index afd6e99c4636c8bea64c965ef793d8aa1bcb8b65..261ff49ad43065b1d55574c31c5fbb15a8c93686 100644
--- a/test/freeflow/rans/test_pipe_laufer.cc
+++ b/test/freeflow/rans/test_pipe_laufer.cc
@@ -238,7 +238,7 @@ int main(int argc, char** argv) try
gnuplot.setOption("set log x");
gnuplot.setOption("set xrange [1:3000]");
gnuplot.addFileToPlot("laufer_re50000_u+y+.csv", "u 1:2 w p t 'Laufer1954a, Re=50000'");
- gnuplot.addFileToPlot(std::string(fileName) + ".csv", "u 13:14 w l");
+ gnuplot.addFileToPlot(std::string(fileName) + ".csv", "u 10:11 w l");
gnuplot.plot(std::string(gnuplotFileName));
}
#endif
diff --git a/test/references/pipe_laufer_zeroeq.vtu b/test/references/pipe_laufer_zeroeq.vtu
index c16176ac3710caebb5f7af8731c53ef288c6d943..4f3ada09cbde459faa7ce787ecb206db38eca506 100644
--- a/test/references/pipe_laufer_zeroeq.vtu
+++ b/test/references/pipe_laufer_zeroeq.vtu
@@ -2,80 +2,8 @@
<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
<UnstructuredGrid>
<Piece NumberOfCells="256" NumberOfPoints="289">
- <CellData Scalars="v_x [m/s]" Vectors="velocity_Air (m/s)">
- <DataArray type="Float32" Name="v_x [m/s]" NumberOfComponents="1" format="ascii">
- 2.07761 1.47958 1.28367 1.25467 1.2256 1.19748 1.1905 1.18952 1.1839 1.17538 1.16979 1.17192
- 1.17724 1.18028 1.18099 1.18075 2.38628 2.14543 1.94733 1.84353 1.78739 1.76159 1.76636 1.77234
- 1.76679 1.75639 1.74958 1.7531 1.75962 1.76261 1.76304 1.76251 2.48263 2.40526 2.27794 2.16452
- 2.08742 2.04048 2.01824 2.00498 1.99072 1.97588 1.97047 1.97997 1.98992 1.99312 1.99343 1.99278
- 2.51407 2.52122 2.48153 2.41111 2.34207 2.28411 2.23834 2.20558 2.18118 2.16111 2.15029 2.1515
- 2.15494 2.15515 2.15383 2.15234 2.52057 2.5554 2.56969 2.55829 2.53194 2.49793 2.45943 2.42442
- 2.39621 2.37341 2.35442 2.33973 2.33042 2.32449 2.31988 2.31677 2.52129 2.56089 2.59214 2.61312
- 2.6256 2.62815 2.61908 2.6043 2.58925 2.57518 2.56046 2.54427 2.53032 2.52023 2.51276 2.50816
- 2.52126 2.56117 2.59479 2.62329 2.64923 2.67126 2.68737 2.69894 2.70788 2.71458 2.71691 2.71332
- 2.70763 2.70291 2.69919 2.69686 2.52119 2.56104 2.59478 2.62384 2.65108 2.67635 2.69959 2.72192
- 2.74377 2.76466 2.78269 2.79612 2.80658 2.81594 2.82425 2.83 2.52119 2.56104 2.59478 2.62384
- 2.65108 2.67635 2.69959 2.72192 2.74377 2.76466 2.78269 2.79612 2.80658 2.81594 2.82425 2.83
- 2.52126 2.56117 2.59479 2.62329 2.64923 2.67126 2.68737 2.69894 2.70788 2.71458 2.71691 2.71332
- 2.70763 2.70291 2.69919 2.69686 2.52129 2.56089 2.59214 2.61312 2.6256 2.62815 2.61908 2.6043
- 2.58925 2.57518 2.56046 2.54427 2.53032 2.52023 2.51276 2.50816 2.52057 2.5554 2.56969 2.55829
- 2.53194 2.49793 2.45943 2.42442 2.39621 2.37341 2.35442 2.33973 2.33042 2.32449 2.31988 2.31677
- 2.51407 2.52122 2.48153 2.41111 2.34207 2.28411 2.23834 2.20558 2.18118 2.16111 2.15029 2.1515
- 2.15494 2.15515 2.15383 2.15234 2.48263 2.40526 2.27794 2.16452 2.08742 2.04048 2.01824 2.00498
- 1.99072 1.97588 1.97047 1.97997 1.98992 1.99312 1.99343 1.99278 2.38628 2.14543 1.94733 1.84353
- 1.78739 1.76159 1.76636 1.77234 1.76679 1.75639 1.74958 1.7531 1.75962 1.76261 1.76304 1.76251
- 2.07761 1.47958 1.28367 1.25467 1.2256 1.19748 1.1905 1.18952 1.1839 1.17538 1.16979 1.17192
- 1.17724 1.18028 1.18099 1.18075
- </DataArray>
- <DataArray type="Float32" Name="dv_x/dx [m/s]" NumberOfComponents="1" format="ascii">
- -0.95686 -0.635157 -0.179922 -0.0464533 -0.0457548 -0.0280812 -0.00636892 -0.00527861 -0.0113137 -0.0112903 -0.0027612 0.0059661
- 0.00668688 0.00299378 0.00037709 -0.000371439 -0.385348 -0.35116 -0.241522 -0.127953 -0.0655552 -0.0168229 0.00859883 0.000348277
- -0.0127609 -0.0137686 -0.00262868 0.00803264 0.00760658 0.00273242 -7.92547e-05 -0.00084692 -0.123792 -0.163751 -0.192587 -0.152414
- -0.0992347 -0.0553436 -0.0283987 -0.0220144 -0.0232791 -0.0162027 0.00326662 0.0155584 0.0105211 0.00280934 -0.000268182 -0.00103498
- 0.0114385 -0.0260362 -0.0880861 -0.111566 -0.101605 -0.0829837 -0.0628222 -0.0457291 -0.0355761 -0.024713 -0.00768423 0.00372169
- 0.00291362 -0.000891487 -0.00224355 -0.00237188 0.0557332 0.0392977 0.00230937 -0.0301996 -0.0482888 -0.0580147 -0.0588047 -0.0505745
- -0.0408131 -0.0334319 -0.0269454 -0.0191991 -0.0121905 -0.00843178 -0.00617655 -0.00497851 0.0633478 0.056677 0.0417843 0.0267666
- 0.0120249 -0.00521208 -0.0190776 -0.0238655 -0.0232978 -0.0230369 -0.0247241 -0.0241065 -0.0192386 -0.0140473 -0.00964972 -0.00736024
- 0.0638551 0.0588229 0.0496947 0.0435467 0.038378 0.0305152 0.0221386 0.0164115 0.0125123 0.00721903 -0.00100371 -0.00742319
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- 0.0341902 0.0311362 0.0251649 0.0191133 0.0158566 0.0141348 0.0112495 0.00919434 0.0637564 0.0588739 0.0502416 0.0450384
- 0.0420084 0.038806 0.0364566 0.0353462 0.0341902 0.0311362 0.0251649 0.0191133 0.0158566 0.0141348 0.0112495 0.00919434
- 0.0638551 0.0588229 0.0496947 0.0435467 0.038378 0.0305152 0.0221386 0.0164115 0.0125123 0.00721903 -0.00100371 -0.00742319
- -0.0083278 -0.00675228 -0.00484026 -0.00372104 0.0633478 0.056677 0.0417843 0.0267666 0.0120249 -0.00521208 -0.0190776 -0.0238655
- -0.0232978 -0.0230369 -0.0247241 -0.0241065 -0.0192386 -0.0140473 -0.00964972 -0.00736024 0.0557332 0.0392977 0.00230937 -0.0301996
- -0.0482888 -0.0580147 -0.0588047 -0.0505745 -0.0408131 -0.0334319 -0.0269454 -0.0191991 -0.0121905 -0.00843178 -0.00617655 -0.00497851
- 0.0114385 -0.0260362 -0.0880861 -0.111566 -0.101605 -0.0829837 -0.0628222 -0.0457291 -0.0355761 -0.024713 -0.00768423 0.00372169
- 0.00291362 -0.000891487 -0.00224355 -0.00237188 -0.123792 -0.163751 -0.192587 -0.152414 -0.0992347 -0.0553436 -0.0283987 -0.0220144
- -0.0232791 -0.0162027 0.00326662 0.0155584 0.0105211 0.00280934 -0.000268182 -0.00103498 -0.385348 -0.35116 -0.241522 -0.127953
- -0.0655552 -0.0168229 0.00859883 0.000348277 -0.0127609 -0.0137686 -0.00262868 0.00803264 0.00760658 0.00273242 -7.92547e-05 -0.00084692
- -0.95686 -0.635157 -0.179922 -0.0464533 -0.0457548 -0.0280812 -0.00636892 -0.00527861 -0.0113137 -0.0112903 -0.0027612 0.0059661
- 0.00668688 0.00299378 0.00037709 -0.000371439
- </DataArray>
- <DataArray type="Float32" Name="dv_x/dy [m/s]" NumberOfComponents="1" format="ascii">
- 71.6647 154.597 154.087 136.72 130.434 130.973 133.701 135.317 135.334 134.897 134.615 134.935
- 135.215 135.202 135.139 135.07 39.1814 89.551 96.1864 88.0195 83.3731 81.5524 80.0763 78.8884
- 78.0526 77.4415 77.4585 78.1704 78.6185 78.6341 78.5962 78.5561 8.83074 25.9671 36.9134 39.2201
- 38.3288 36.1063 32.6142 29.9373 28.6342 27.9666 27.6889 27.53 27.3165 27.1246 27.0035 26.9377
- 1.87278 7.41083 14.4002 19.4353 21.9405 22.5785 21.7757 20.7025 20.0136 19.6207 18.9506 17.7568
- 16.8062 16.3555 16.1127 15.991 0.254612 1.39841 3.89971 7.12168 9.99591 12.1292 13.4232 14.057
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