diff --git a/A/plotPressure.sh b/A/plotPressure.sh new file mode 100755 index 0000000000000000000000000000000000000000..5adec1a415ab9cd6d46bd352d4bc60d9e197f54b --- /dev/null +++ b/A/plotPressure.sh @@ -0,0 +1,28 @@ +#! /bin/bash +gnuplot -p << EOF +set grid +set xlabel 'Time [s]' font ",12" +set ylabel 'Pressure [Pa]' font ",12" offset -3 +set key center bottom +set encoding utf8 +set xtics font ",12" +set ytics font ",12" +set key font ",14" +set format y "%.1t*10^%T"; +set lmargin 15 + +#set xrange [6.8:8.2] +set yrange [-350000:350000] +#set yrange [220000:320000] + + +plot "results/watchpointI.txt" using 1:2 with lines dt 1 lc rgb "grey" lw 2 title "Crank-Nicolson θ = 0.5",\ + "results/watchpointII.txt" using 1:2 with lines dt 3 lc rgb "black" lw 2 title "Crank-Nicolson θ = 0.55",\ + "results/watchpointIII.txt" using 1:2 with lines dt 2 lc rgb "dark-grey" lw 2 title "Backward Euler" + +#plot "results/watchpointI.txt" using 1:2 with linespoints pi 50 dt 1 pt 6 lt -1 title "Crank-Nicolson θ = 0.5",\ +# "results/watchpointII.txt" using 1:2 with linespoints pi 50 dt 2 pt 6 lt -1title "Crank-Nicolson θ = 0.5",\ +# "results/watchpointIII.txt" using 1:2 with linespoints pi 50 dt 3 pt 6 lt -1 title "Backward Euler" + +EOF + diff --git a/A/plotVelocity.sh b/A/plotVelocity.sh new file mode 100755 index 0000000000000000000000000000000000000000..0c9133dc33f500d00f912f52e18fa4e8791006fc --- /dev/null +++ b/A/plotVelocity.sh @@ -0,0 +1,8 @@ +#! /bin/bash +gnuplot -p << EOF +set grid +set xlabel 'Time [s]' +set ylabel 'Velocity' +plot "watchpoint.txt" using 1:3 with lines title "" +EOF + diff --git a/A/results/README.md b/A/results/README.md new file mode 100644 index 0000000000000000000000000000000000000000..ec2285631e2943811855a51b975dd14098ef5705 --- /dev/null +++ b/A/results/README.md @@ -0,0 +1,3 @@ +I: normal CN, theta=0.5 +II: theta=0.55 +III: theta=1.0 -> BE diff --git a/A/results/watchpointI.txt b/A/results/watchpointI.txt new file mode 100644 index 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2.636706e+05; 9.143187e-01 +1.994000e+01; 2.628371e+05; 9.133931e-01 +1.994500e+01; 2.619912e+05; 9.124695e-01 +1.995000e+01; 2.611328e+05; 9.115477e-01 +1.995500e+01; 2.602619e+05; 9.106280e-01 +1.996000e+01; 2.593786e+05; 9.097103e-01 +1.996500e+01; 2.584826e+05; 9.087947e-01 +1.997000e+01; 2.575741e+05; 9.078813e-01 +1.997500e+01; 2.566531e+05; 9.069702e-01 +1.998000e+01; 2.557194e+05; 9.060615e-01 +1.998500e+01; 2.547731e+05; 9.051551e-01 +1.999000e+01; 2.538142e+05; 9.042512e-01 +1.999500e+01; 2.528426e+05; 9.033499e-01 diff --git a/A/sonicLiquid.py b/A/sonicLiquid.py new file mode 100644 index 0000000000000000000000000000000000000000..2d9e15647094fcfeea91088746a61abd3e8adf42 --- /dev/null +++ b/A/sonicLiquid.py @@ -0,0 +1,67 @@ +#! /usr/bin/python3 + +from nutils import * +import numpy, itertools, treelog + +@function.replace +def subs0(f): + if isinstance(f, function.Argument) and f._name == 'lhs': + return function.Argument(name='lhs0', shape=f.shape, nderiv=f._nderiv) + +def main(nelems=200, timestep=.005, refdensity=1e3, refpressure=101325., psi=1e-6, viscosity=1e-3, theta=1.0): + + domain, geom = mesh.rectilinear([numpy.linspace(0, 1000, nelems+1)]) + bezier = domain.sample('bezier', 2) + + ns = function.Namespace() + ns._functions['t'] = lambda f: theta * f + (1-theta) * subs0(f) + ns._functions_nargs['t'] = 1 + ns._functions['δt'] = lambda f: (f - subs0(f)) / timestep + ns._functions_nargs['δt'] = 1 + ns.x = geom + ns.ρref = refdensity + ns.pref = refpressure + ns.pin = 98100 + ns.μ = viscosity + ns.ψ = psi + ns.ρbasis, ns.ubasis = function.chain([domain.basis('std', degree=1), domain.basis('std', degree=2).vector(domain.ndims)]) + ns.ρ = 'ρref + ρbasis_n ?lhs_n' # density is shifted by ref density + ns.u_i = 'ubasis_ni ?lhs_n' + ns.p = 'pref + (ρ - ρref) / ψ' # pressure-density connection, see equ (8) + ns.σ_ij = 'μ (u_i,j + u_j,i) - p δ_ij' # diffusive term and pressure gradient + ns.h = 1 / nelems + ns.k = 'ρ h / μ' # needs work, stabilization coeff + + res = domain.integral('ρbasis_n (δt(ρ) + t((ρ u_k)_,k)) d:x' @ ns, degree=4) # mass balance + res += domain.integral('(ubasis_ni (δt(ρ u_i) + t((ρ u_i u_j)_,j)) + ubasis_ni,j t(σ_ij)) d:x' @ ns, degree=4) # momentum balance + res += domain.boundary['left'].integral('pin ubasis_ni n_i d:x' @ ns, degree=4) # pressure set at inlet + #res += domain.integral('k ubasis_ni,j (u_j / sqrt(u_k u_k)) (δρu_i / δt + (ρ u_i u_j - σ_ij)_,j) d:x' @ ns, degree=4) # SUPG stabilization + + lhs = numpy.zeros(res.shape) + t = 0 + + f = open("watchpoint.txt", "w") + + sqr = domain.boundary['right'].integral('(u_0 - 1)^2' @ ns, degree=4) + cons0 = solver.optimize('lhs', sqr, droptol=1e-14) + + for istep in itertools.count(): + with log.context('timestep', istep): + + x, p, ρ, u = bezier.eval(['x_i', 'p', 'ρ', 'u_i'] @ ns, lhs=lhs) + f.write("%e; %e; %e\n" % (t, p[399], u[199])) + f.flush() + + cons = min(.2 * t, 1) * cons0 + + lhs = solver.newton('lhs', res, constrain=cons, arguments=dict(lhs0=lhs), lhs0=lhs).solve(1e-8) + + t += timestep + + if t>=20: + break + f.close() + + +if __name__ == '__main__': + cli.run(main) diff --git a/B/Allclean b/B/Allclean new file mode 100755 index 0000000000000000000000000000000000000000..22d772324d68f3366a434ddf4adce4712c3b6b40 --- /dev/null +++ b/B/Allclean @@ -0,0 +1,29 @@ +#!/bin/sh +cd ${0%/*} || exit 1 # Run from this directory + +echo "Cleaning..." + +# Source tutorial clean functions +. $WM_PROJECT_DIR/bin/tools/CleanFunctions + +# Participant 1: Fluid1 +Participant1="Fluid1" +cd ${Participant1} + # Clean the case + cleanCase + rm -rfv 0 + # Create an empty .foam file for ParaView + # Note: ".foam" triggers the native OpenFOAM reader of ParaView. + # Change to ".OpenFOAM" to use the OpenFOAM reader provided with OpenFOAM. + touch ${Participant1}.foam +cd .. +# Remove the log files +rm -fv ${Participant1}_blockMesh.log +rm -fv ${Participant1}_checkMesh.log +rm -fv ${Participant1}_potentialFoam.log +rm -fv ${Participant1}_decomposePar.log +rm -fv ${Participant1}.log +rm -fv ${Participant1}_reconstructPar.log + +echo "Cleaning complete!" +#------------------------------------------------------------------------------ diff --git a/B/Fluid1/0.orig/U b/B/Fluid1/0.orig/U new file mode 100644 index 0000000000000000000000000000000000000000..a018bee3147df7f584197028f4a08e9d86101f09 --- /dev/null +++ b/B/Fluid1/0.orig/U @@ -0,0 +1,72 @@ +FoamFile +{ + version 2.0; + format ascii; + class volVectorField; + location "0"; + object U; +} +// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // + +dimensions [0 1 -1 0 0 0 0]; + +internalField uniform (0 0 0); + +boundaryField +{ + inlet + { + type zeroGradient; + } + outlet + { + outOfBounds clamp; + // Time-varying outlet velocity + type uniformFixedValue; + uniformValue table + ( + ( 0 ( 0 0 0 ) ) + ( 5 ( 0 1 0 ) ) + ( 100 ( 0 1 0 ) ) + ); + } + xEmpty1 + { + // type fixedValue; + // value uniform (0 0 0); + + // type empty; + type symmetryPlane; + } + + xEmpty2 + { + // type fixedValue; + // value uniform (0 0 0); + + // type empty; + type symmetryPlane; + } + + yEmpty1 + { + //type fixedValue; + // value uniform (0 0 0); + + //type empty; + type symmetryPlane; + } + + yEmpty2 + { + //type fixedValue; + // value uniform (0 0 0); + + // type empty; + type symmetryPlane; + } + +} + + +// ************************************************************************* // diff --git a/B/Fluid1/0.orig/p b/B/Fluid1/0.orig/p new file mode 100644 index 0000000000000000000000000000000000000000..c22b42c41df25634787483c6c1c30c43084eff43 --- /dev/null +++ b/B/Fluid1/0.orig/p @@ -0,0 +1,59 @@ +FoamFile +{ + version 2.0; + format ascii; + class volScalarField; + object p; +} +// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // + +dimensions [1 -1 -2 0 0 0 0]; + +internalField uniform 98100; + +boundaryField +{ + inlet + { + type fixedValue; + value uniform 98100; + } + + outlet + { + type zeroGradient; + value uniform 98100; + } + + xEmpty1 + { + // type zeroGradient; + // type empty; + type symmetryPlane; + } + + xEmpty2 + { + // type zeroGradient; + // type empty; + type symmetryPlane; + } + + yEmpty1 + { + //type zeroGradient; + // type empty; + type symmetryPlane; + } + + + yEmpty2 + { + // type zeroGradient; + // type empty; + type symmetryPlane; + } + +} + +// ************************************************************************* // diff --git a/B/Fluid1/Fluid1.foam b/B/Fluid1/Fluid1.foam new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/B/Fluid1/constant/thermodynamicProperties b/B/Fluid1/constant/thermodynamicProperties new file mode 100644 index 0000000000000000000000000000000000000000..ad66894019be987406ff14fac1219f48dabe5a22 --- /dev/null +++ b/B/Fluid1/constant/thermodynamicProperties @@ -0,0 +1,25 @@ +/*--------------------------------*- C++ -*----------------------------------*\ +| ========= | | +| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox | +| \\ / O peration | Version: 5 | +| \\ / A nd | Web: www.OpenFOAM.org | +| \\/ M anipulation | | +\*---------------------------------------------------------------------------*/ +FoamFile +{ + version 2.0; + format ascii; + class dictionary; + location "constant"; + object thermodynamicProperties; +} +// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // + +rho0 rho0 [1 -3 0 0 0 0 0] 1000; + +p0 p0 [1 -1 -2 0 0 0 0] 101325; + +psi psi [0 -2 2 0 0 0 0] 1e-6; + + +// ************************************************************************* // diff --git a/B/Fluid1/constant/transportProperties b/B/Fluid1/constant/transportProperties new file mode 100644 index 0000000000000000000000000000000000000000..4872f8e62814c0b38fd09ded1c33f3122307310d --- /dev/null +++ b/B/Fluid1/constant/transportProperties @@ -0,0 +1,13 @@ +FoamFile +{ + version 2.0; + format ascii; + class dictionary; + location "constant"; + object transportProperties; +} +// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // + +mu mu [1 -1 -1 0 0 0 0] 1e-3; + +// ************************************************************************* // diff --git a/B/Fluid1/constant/turbulenceProperties b/B/Fluid1/constant/turbulenceProperties new file mode 100644 index 0000000000000000000000000000000000000000..a74ee048f1e018d4822c766cd02c4b585bdafa1e --- /dev/null +++ b/B/Fluid1/constant/turbulenceProperties @@ -0,0 +1,13 @@ +FoamFile +{ + version 2.0; + format ascii; + class dictionary; + location "constant"; + object turbulenceProperties; +} +// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // + +simulationType laminar; + +// ************************************************************************* // diff --git a/B/Fluid1/system/blockMeshDict b/B/Fluid1/system/blockMeshDict new file mode 100644 index 0000000000000000000000000000000000000000..ef7b2bb85a6dc9ac31c64c5f981c9e8cca57213f --- /dev/null +++ b/B/Fluid1/system/blockMeshDict @@ -0,0 +1,108 @@ +FoamFile +{ + version 2.0; + format ascii; + class dictionary; + location "constant/polyMesh"; + object blockMeshDict; +} + +convertToMeters 1; + +vertices + ( + ( -0.5 0 -0.5 ) //0 + ( 0.5 0 -0.5 ) //1 + ( 0.5 1000 -0.5 ) //2 + ( -0.5 1000 -0.5 ) //3 + ( -0.5 0 0.5 ) //4 + ( 0.5 0 0.5 ) //5 + ( 0.5 1000 0.5 ) //6 + ( -0.5 1000 0.5 ) //7 + ); + + blocks +( + hex (0 1 2 3 4 5 6 7) (10 200 10) simpleGrading (1 1 1) //1 +); + + + edges + ( + ); + +boundary +( + outlet + { + type patch; + faces + ( + (3 7 6 2) + ); + } + + inlet + { + type patch; + faces + ( + (0 1 5 4) + ); + } + + xEmpty1 + { + // type empty; + //type wall; + type symmetryPlane; + + faces + ( + (4 7 3 0) + ); + } + + xEmpty2 + { + // type empty; + //type wall; + type symmetryPlane; + + faces + ( + (1 2 6 5) + ); + } + yEmpty1 + { + // type empty; + //type wall; + type symmetryPlane; + faces + ( + (0 3 2 1) + ); + } + + yEmpty2 + { + // type empty; + //type wall; + type symmetryPlane; + faces + ( + (5 6 7 4) + ); + } + +); + + mergePatchPairs + ( + ); + + // ************************************************************************* // + + + diff --git a/B/Fluid1/system/controlDict b/B/Fluid1/system/controlDict new file mode 100644 index 0000000000000000000000000000000000000000..0c404192b86a162a9ab899f6ff8336a230e22ef8 --- /dev/null +++ b/B/Fluid1/system/controlDict @@ -0,0 +1,50 @@ +FoamFile +{ + version 2.0; + format ascii; + class dictionary; + location "system"; + object controlDict; +} +// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // + +application sonicLiquidFoam; + +startFrom startTime; + +startTime 0; + +stopAt endTime; + +endTime 20.0; + +deltaT 0.005; + +writeControl adjustableRunTime; + +writeInterval 100; + +purgeWrite 0; + +writeFormat ascii; + +writePrecision 10; + +writeCompression off; + +timeFormat general; + +timePrecision 6; + +functions{#includeFunc probes} + + +/*functions +{ + preCICE_Adapter + { + type preciceAdapterFunctionObject; + libs ("libpreciceAdapterFunctionObject.so"); + } +} +*/ diff --git a/B/Fluid1/system/fvSchemes b/B/Fluid1/system/fvSchemes new file mode 100644 index 0000000000000000000000000000000000000000..aca1456cfb241658f67e22dfd26363161f2ef7b9 --- /dev/null +++ b/B/Fluid1/system/fvSchemes @@ -0,0 +1,52 @@ +/*--------------------------------*- C++ -*----------------------------------*\ +| ========= | | +| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox | +| \\ / O peration | Version: 5 | +| \\ / A nd | Web: www.OpenFOAM.org | +| \\/ M anipulation | | +\*---------------------------------------------------------------------------*/ +FoamFile +{ + version 2.0; + format ascii; + class dictionary; + location "system"; + object fvSchemes; +} +// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // + +ddtSchemes +{ + //default Euler; + default CrankNicolson 0.45; +} + +gradSchemes +{ + default Gauss linear; +} + +divSchemes +{ + default none; + div(phi,U) Gauss limitedLinearV 1; + div(phid,p) Gauss limitedLinear 1; +} + +laplacianSchemes +{ + default Gauss linear corrected; +} + +interpolationSchemes +{ + default linear; +} + +snGradSchemes +{ + default corrected; +} + + +// ************************************************************************* // diff --git a/B/Fluid1/system/fvSolution b/B/Fluid1/system/fvSolution new file mode 100644 index 0000000000000000000000000000000000000000..b8eb36c8620675f988c0f77ffe50670aec313a52 --- /dev/null +++ b/B/Fluid1/system/fvSolution @@ -0,0 +1,55 @@ +/*--------------------------------*- C++ -*----------------------------------*\ +| ========= | | +| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox | +| \\ / O peration | Version: 5 | +| \\ / A nd | Web: www.OpenFOAM.org | +| \\/ M anipulation | | +\*---------------------------------------------------------------------------*/ +FoamFile +{ + version 2.0; + format ascii; + class dictionary; + location "system"; + object fvSolution; +} +// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // + +solvers +{ + "p.*" + { + solver PBiCG; + preconditioner DILU + //smoother symGaussSeidel; + tolerance 1e-06; + relTol 0.01; + } + + "U.*" + { + $p; + solver PBiCG; + preconditioner DILU; + tolerance 1e-05; + relTol 0.1; + } + + "rho.*" + { + solver PCG; + preconditioner DIC; + tolerance 1e-05; + relTol 0.1; + } +} + +PIMPLE +{ + nOuterCorrectors 4; + nCorrectors 2; + nNonOrthogonalCorrectors 0; +} + + +// ************************************************************************* // diff --git a/B/Fluid1/system/probes b/B/Fluid1/system/probes new file mode 100644 index 0000000000000000000000000000000000000000..e688e017774765b46ab6e11bed35dbbfcf70b406 --- /dev/null +++ b/B/Fluid1/system/probes @@ -0,0 +1,22 @@ +/*--------------------------------*- C++ -*----------------------------------*\ + ========= | + \\ / F ield | OpenFOAM: The Open Source CFD Toolbox + \\ / O peration | + \\ / A nd | Web: www.OpenFOAM.org + \\/ M anipulation | +------------------------------------------------------------------------------- +Description + Writes out values of fields from cells nearest to specified locations. + +\*---------------------------------------------------------------------------*/ + +#includeEtc "caseDicts/postProcessing/probes/probes.cfg" + +fields (p U); +probeLocations +( + (0 999 0) + (0 500 0) +); + +// ************************************************************************* // diff --git a/B/Fluid1/system/probesDict b/B/Fluid1/system/probesDict new file mode 100644 index 0000000000000000000000000000000000000000..936fb03e91356aad81753ab15d49915d1eca4343 --- /dev/null +++ b/B/Fluid1/system/probesDict @@ -0,0 +1,31 @@ +/*--------------------------------*- C++ -*----------------------------------*\ +| ========= | | +| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox | +| \\ / O peration | Version: 5 | +| \\ / A nd | Web: www.OpenFOAM.org | +| \\/ M anipulation | | +\*---------------------------------------------------------------------------*/ +FoamFile +{ + version 2.0; + format ascii; + class dictionary; + object probesDict; +} +// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // + +// Fields to be probed. runTime modifiable! +fields +( + p U +); + +// Locations to be probed. runTime modifiable! +probeLocations +( + (0 999 0) + (0 500 0) +); + + +// ************************************************************************* // diff --git a/B/plotPressure.sh b/B/plotPressure.sh new file mode 100755 index 0000000000000000000000000000000000000000..208628258aec6077574ad4cbfa434ee09a3065c4 --- /dev/null +++ b/B/plotPressure.sh @@ -0,0 +1,12 @@ +#! /bin/bash +gnuplot -p << EOF +set grid +set xlabel 'Time [s]' +set ylabel 'Pressure' +set xrange [6.8:8.2] +set yrange [280000:310000] + +plot "results/I/p" using 1:2 with lines title "CN 0.45", \ + "results/II/p" using 1:2 with lines title "CN 0.5" +EOF + diff --git a/B/plotVelocity.sh b/B/plotVelocity.sh new file mode 100755 index 0000000000000000000000000000000000000000..7984c2ce47f248bde43695120c0ec68884262783 --- /dev/null +++ b/B/plotVelocity.sh @@ -0,0 +1,9 @@ +#! /bin/bash +gnuplot -p << EOF +set grid +set xlabel 'Time [s]' +set ylabel 'Velocity' +plot "results/I/U" using 1:6 with lines title "CN 0.45", \ + "results/II/U" using 1:6 with lines title "CN 0.5" +EOF + diff --git a/B/results/I/U b/B/results/I/U new file mode 100644 index 0000000000000000000000000000000000000000..10a32cd6b1f4f026a471b24ca1c30598acc93411 --- /dev/null +++ b/B/results/I/U @@ -0,0 +1,4004 @@ +# Probe 0 (0 999 0) +# Probe 1 (0 500 0) +# Probe 0 1 +# Time + 0.005 (-1.133596971e-12 0.0001909823775 -1.13869049e-12) (2.190070188e-13 2.296481551e-15 -2.204622117e-13) + 0.01 (2.830016956e-12 0.0005499690493 2.5182496e-12) (3.629911521e-12 4.561601121e-15 -3.631316534e-12) + 0.015 (2.84912635e-11 0.001097098707 2.995453652e-11) (5.759563668e-13 3.621525582e-15 -5.75630198e-13) + 0.02 (-5.273442095e-11 0.001730353734 -5.516358938e-11) (8.926872985e-13 -3.960626859e-15 -8.921855019e-13) + 0.025 (-3.152797265e-11 0.002383387459 -5.169123556e-11) (3.751670967e-12 -1.043570119e-14 -3.750391393e-12) + 0.03 (-1.084453348e-10 0.003035835115 -1.327426387e-10) (-7.156128388e-12 -1.274747165e-14 7.155350617e-12) + 0.035 (-7.987028289e-11 0.003685309227 -2.376740446e-11) (-2.801428386e-12 -7.666829682e-15 2.801528752e-12) + 0.04 (-7.687516678e-11 0.004333951699 -6.9368797e-11) (-2.94303386e-12 4.312274828e-16 2.94052491e-12) + 0.045 (-7.743607475e-11 0.004984910014 -9.443099992e-11) (5.576010756e-12 6.934527622e-15 -5.576086016e-12) + 0.05 (1.745194835e-10 0.005640409101 8.837236835e-11) (3.392426014e-11 9.649299643e-15 -3.392353253e-11) + 0.055 (-1.842771864e-10 0.006301086748 -1.685885821e-10) (-4.290455406e-11 8.563782845e-15 4.290282288e-11) + 0.06 (-9.965816506e-11 0.00696673966 1.958759588e-12) (2.470112712e-11 8.858585576e-15 -2.470024898e-11) + 0.065 (2.6428983e-11 0.007637055413 7.192839172e-11) (-2.221703279e-11 1.206378075e-14 2.221648083e-11) + 0.07 (5.210792373e-10 0.008311721762 5.897237601e-10) (-4.673630884e-11 1.133343852e-14 4.673741278e-11) + 0.075 (2.10170228e-10 0.008990382481 1.317089165e-10) (3.52476421e-12 1.004446087e-14 -3.522305431e-12) + 0.08 (2.239868204e-10 0.009672716115 -3.317593976e-10) (2.054167762e-11 9.543061139e-15 -2.05417278e-11) + 0.085 (3.587765949e-10 0.01035849087 1.403110555e-10) (4.325841762e-11 9.955079291e-15 -4.325608429e-11) + 0.09 (1.083955882e-10 0.01104752239 8.345830328e-10) (7.184377939e-12 1.260477522e-14 -7.181467555e-12) + 0.095 (1.511755729e-10 0.01173963093 4.360216039e-10) (-4.976143821e-11 1.321398186e-14 4.97628934e-11) + 0.1 (3.848879047e-10 0.0124346472 1.401407823e-10) (-2.369759354e-11 1.372361419e-14 2.36996007e-11) + 0.105 (-3.21120525e-10 0.01313242562 -2.580273219e-10) (-1.733389475e-11 1.68315872e-14 1.733033202e-11) + 0.11 (-6.331028381e-10 0.01383283752 -6.674960271e-10) (4.076117409e-11 1.680610562e-14 -4.07549017e-11) + 0.115 (-5.643640801e-10 0.01453576759 -4.495342704e-10) (-1.098783011e-10 1.640349618e-14 1.0988219e-10) + 0.12 (-3.466792084e-10 0.01524110082 -3.028855528e-10) (7.825307668e-11 1.746901982e-14 -7.825179712e-11) + 0.125 (-2.561055998e-10 0.01594872491 -2.40466997e-10) (-6.741610312e-11 2.446039099e-14 6.741582713e-11) + 0.13 (-1.288831377e-10 0.01665854209 -1.302317353e-10) (6.227313932e-11 3.625053827e-14 -6.227130778e-11) + 0.135 (-4.64733189e-11 0.01737046851 -1.465134672e-11) (-6.20466811e-11 3.078257589e-14 6.204735852e-11) + 0.14 (3.470687358e-11 0.01808442564 3.313751482e-11) (5.917645559e-11 1.238681027e-14 -5.917590363e-11) + 0.145 (7.229207891e-11 0.01880033512 9.267097442e-11) (-5.630309818e-11 1.070267171e-14 5.630410176e-11) + 0.15 (1.217992428e-10 0.01951812084 1.274545937e-10) (5.377464064e-11 3.255923295e-14 -5.377263348e-11) + 0.155 (1.540722719e-10 0.02023771327 1.71240473e-10) (-5.206353577e-11 5.377992987e-14 5.206448917e-11) + 0.16 (-1.183155787e-09 0.02095905337 -1.180515437e-09) (4.134886996e-11 4.554623224e-14 -4.13470886e-11) + 0.165 (1.932022431e-09 0.02168208063 1.934253882e-09) (2.866946674e-11 7.558241066e-15 -2.866851334e-11) + 0.17 (1.050611444e-10 0.02240673382 1.144694333e-10) (-2.159471684e-11 -1.789436374e-14 2.15964982e-11) + 0.175 (1.609338764e-09 0.0231329618 1.625754227e-09) (-6.401416063e-11 -1.010420487e-13 6.401611762e-11) + 0.18 (1.752560084e-09 0.02386071802 1.763363105e-09) (-3.63021042e-11 -1.152588295e-13 3.630483896e-11) + 0.185 (1.325496035e-09 0.02458995557 1.322564144e-09) (4.301321327e-11 7.530799832e-15 -4.301153227e-11) + 0.19 (1.179674381e-09 0.02532062765 1.180217525e-09) (1.957002508e-11 1.370444392e-13 -1.956902151e-11) + 0.195 (9.023248488e-10 0.02605269049 9.095472198e-10) (-2.565142659e-11 1.687467043e-13 2.565343374e-11) + 0.2 (6.427366523e-10 0.02678610422 6.494854147e-10) (-1.923092455e-11 1.330967493e-13 1.923137614e-11) + 0.205 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