diff --git a/include/teqp/algorithms/VLE.hpp b/include/teqp/algorithms/VLE.hpp
index dd0fb7b4ebe81fde3bfa1c343ab0242c2ac24c3f..a72a8c2df6be09ba96364faea1dc7a1746c5157a 100644
--- a/include/teqp/algorithms/VLE.hpp
+++ b/include/teqp/algorithms/VLE.hpp
@@ -13,10 +13,15 @@ private:
TYPE m_T;
EigenMatrix J;
EigenArray y;
+
public:
std::size_t icall = 0;
+ double Rr, R0;
- IsothermPureVLEResiduals(const Model& model, TYPE T) : m_model(model), m_T(T) {};
+ IsothermPureVLEResiduals(const Model& model, TYPE T) : m_model(model), m_T(T) {
+ Rr = m_model.R;
+ R0 = m_model.R;
+ };
const auto& get_errors() { return y; };
@@ -33,22 +38,23 @@ public:
const TYPE &T = m_T;
const TYPE R = m_model.R;
+ double R0_over_Rr = R0 / Rr;
auto derL = tdx::template get_Ar0n<2>(m_model, T, rhomolarL, molefracs);
- auto pL = rhomolarL*R*T*(1+derL[1]);
- auto dpLdrho = R*T*(1 + 2*derL[1] + derL[2]);
- auto hatmurL = id::build_Psir_gradient_autodiff(m_model, T, rhovecL)[0] + R*T*log(rhomolarL);
- auto dhatmurLdrho = id::build_Psir_Hessian_autodiff(m_model, T, rhovecL)(0,0) + R*T/rhomolarL;
+ auto pRTL = rhomolarL*(R0_over_Rr + derL[1]); // p/(R*T)
+ auto dpRTLdrhoL = R0_over_Rr + 2*derL[1] + derL[2];
+ auto hatmurL = derL[1] + derL[0] + R0_over_Rr*log(rhomolarL);
+ auto dhatmurLdrho = (2*derL[1] + derL[2])/rhomolarL + R0_over_Rr/rhomolarL;
auto derV = tdx::template get_Ar0n<2>(m_model, T, rhomolarV, molefracs);
- auto pV = rhomolarV*R*T*(1 + derV[1]);
- auto dpVdrho = R*T*(1 + 2*derV[1] + derV[2]);
- auto hatmurV = id::build_Psir_gradient_autodiff(m_model, T, rhovecV)[0] + R*T*log(rhomolarV);
- auto dhatmurVdrho = id::build_Psir_Hessian_autodiff(m_model, T, rhovecV)(0,0) + R*T/rhomolarV;
+ auto pRTV = rhomolarV*(R0_over_Rr + derV[1]); // p/(R*T)
+ auto dpRTVdrhoV = R0_over_Rr + 2*derV[1] + derV[2];
+ auto hatmurV = derV[1] + derV[0] + R0_over_Rr *log(rhomolarV);
+ auto dhatmurVdrho = (2*derV[1] + derV[2])/rhomolarV + R0_over_Rr/rhomolarV;
- y(0) = pL - pV;
- J(0, 0) = dpLdrho;
- J(0, 1) = -dpVdrho;
+ y(0) = pRTL - pRTV;
+ J(0, 0) = dpRTLdrhoL;
+ J(0, 1) = -dpRTVdrhoV;
y(1) = hatmurL - hatmurV;
J(1, 0) = dhatmurLdrho;
@@ -60,10 +66,19 @@ public:
auto Jacobian(const EigenArray& rhovec){
return J;
}
+ //auto numJacobian(const EigenArray& rhovec) {
+ // EigenArray plus0 = rhovec, plus1 = rhovec;
+ // double dr = 1e-6 * rhovec[0];
+ // plus0[0] += dr; plus1[1] += dr;
+ // EigenMatrix J;
+ // J.col(0) = (call(plus0) - call(rhovec))/dr;
+ // J.col(1) = (call(plus1) - call(rhovec))/dr;
+ // return J;
+ //}
};
template<typename Residual, typename Scalar>
-auto do_pure_VLE_T(Residual &resid, Scalar T, Scalar rhoL, Scalar rhoV, int maxiter) {
+auto do_pure_VLE_T(Residual &resid, Scalar rhoL, Scalar rhoV, int maxiter) {
auto rhovec = (Eigen::ArrayXd(2) << rhoL, rhoV).finished();
auto r0 = resid.call(rhovec);
auto J = resid.Jacobian(rhovec);
@@ -81,7 +96,31 @@ auto do_pure_VLE_T(Residual &resid, Scalar T, Scalar rhoL, Scalar rhoV, int maxi
if (((rhovecnew - rhovec).cwiseAbs() < std::numeric_limits<Scalar>::min()).all()) {
break;
}
- rhovec += v;
+ rhovec = rhovecnew;
}
- return std::make_tuple(rhovec[0], rhovec[1]);
+ return (Eigen::ArrayXd(2) << rhovec[0], rhovec[1]).finished();
+}
+
+template<typename Model, typename Scalar>
+auto extrapolate_from_critical(const Model& model, const Scalar Tc, const Scalar rhoc, const Scalar T) {
+
+ using tdx = TDXDerivatives<Model>;
+ auto z = (Eigen::ArrayXd(1) << 1.0).finished();
+ auto R = model.R;
+ auto ders = tdx::get_Ar0n<4>(model, Tc, rhoc, z);
+ auto dpdrho = R*Tc*(1 + 2 * ders[1] + ders[2]); // Should be zero
+ auto d2pdrho2 = R*Tc/rhoc*(2 * ders[1] + 4 * ders[2] + ders[3]); // Should be zero
+ auto d3pdrho3 = R*Tc/(rhoc*rhoc)*(6 * ders[2] + 6 * ders[3] + ders[4]);
+ auto Ar11 = tdx::get_Ar11(model, Tc, rhoc, z);
+ auto Ar12 = tdx::get_Ar12(model, Tc, rhoc, z);
+ auto d2pdrhodT = R * (1 + 2 * ders[1] + ders[2] - 2 * Ar11 - Ar12);
+ auto Brho = sqrt(6*d2pdrhodT*Tc/d3pdrho3);
+
+ auto drhohat_dT = Brho / Tc;
+ auto dT = T - Tc;
+
+ auto drhohat = dT * drhohat_dT;
+ auto rholiq = -drhohat/sqrt(1 - T/Tc) + rhoc;
+ auto rhovap = drhohat/sqrt(1 - T/Tc) + rhoc;
+ return (Eigen::ArrayXd(2) << rholiq, rhovap).finished();
}
\ No newline at end of file
diff --git a/include/teqp/derivs.hpp b/include/teqp/derivs.hpp
index dbdf8a7dac7d72cec8a43353f3cd656e4b2d9473..1eb6e3f880fa0a1929c52075ce552b0e4a60ff4e 100644
--- a/include/teqp/derivs.hpp
+++ b/include/teqp/derivs.hpp
@@ -140,7 +140,7 @@ struct TDXDerivatives {
autodiff::HigherOrderDual<Nderiv, double> rhodual = rho;
auto f = [&model, &T, &molefrac](const auto& rho_) { return eval(model.alphar(T, rho_, molefrac)); };
auto ders = derivatives(f, wrt(rhodual), at(rhodual));
- for (auto n = 1; n <= Nderiv; ++n) {
+ for (auto n = 0; n <= Nderiv; ++n) {
o[n] = pow(rho, n)*ders[n];
}
return o;
diff --git a/include/teqp/models/cubicsuperancillary.hpp b/include/teqp/models/cubicsuperancillary.hpp
new file mode 100644
index 0000000000000000000000000000000000000000..9077a6d1d95b850620935cc15ec22d5464c0929f
--- /dev/null
+++ b/include/teqp/models/cubicsuperancillary.hpp
@@ -0,0 +1,3845 @@
+#include <vector>
+
+namespace CubicSuperAncillary {
+
+struct Chebyshev{
+public:
+ const std::vector<double> coeff;
+ const double xmin, xmax;
+ // Evaluate the expansion with Clenshaw's method
+ double y(double x) const{
+ // Scale to (-1, 1)
+ double xscaled = (2*x - (xmax + xmin)) / (xmax - xmin);
+ int Norder = static_cast<int>(coeff.size()) - 1;
+ double u_k = 0, u_kp1 = coeff[Norder], u_kp2 = 0;
+ for (int k = Norder-1; k > 0; k--){ // k must be signed!
+ // Do the recurrent calculation
+ u_k = 2.0*xscaled*u_kp1 - u_kp2 + coeff[k];
+ // Update the values
+ u_kp2 = u_kp1; u_kp1 = u_k;
+ }
+ return coeff[0] + xscaled*u_kp1 - u_kp2;
+ };
+};
+
+// https://proquest.safaribooksonline.com/9780321637413
+// https://web.stanford.edu/class/archive/cs/cs107/cs107.1202/lab1/
+int midpoint_Knuth(int x, int y) {
+ return (x & y) + ((x ^ y) >> 1);
+};
+
+struct SuperAncillary{
+public:
+
+ const std::vector<Chebyshev> exps;
+
+ int get_index(double x) const{
+ int iL = 0, iR = static_cast<int>(exps.size()) - 1, iM;
+ while (iR - iL > 1) {
+ iM = midpoint_Knuth(iL, iR);
+ if (x >= exps[iM].xmin) {
+ iL = iM;
+ }
+ else {
+ iR = iM;
+ }
+ }
+ return (x < exps[iL].xmax) ? iL : iR;
+ };
+
+ /// Evaluate the SuperAncillary
+ double y(double x) const{
+ // Bisection to find the expansion
+ // we need
+ auto i = get_index(x);
+ // Evaluate the expansion
+ return exps[i].y(x);
+ }
+};
+
+const auto vdW_p = SuperAncillary{
+{
+ {
+ {
+ 8.369016487003571e-13,
+ 1.3838182749488314e-12,
+ 8.006631877160537e-13,
+ 3.3527912014616007e-13,
+ 1.043509859614108e-13,
+ 2.4518354339464807e-14,
+ 4.362454910953413e-15,
+ 5.800290149785568e-16,
+ 5.5246311563342216e-17,
+ 3.341712352615597e-18,
+ 6.943507182585673e-20,
+ -6.6172300100790814e-21,
+ -4.799249815587726e-22,
+ 8.197853768324654e-24,
+ 1.6972506557505968e-24,
+ -1.4268299756055458e-26,
+ -5.664810160392086e-27,
+ 4.437342591868191e-31,
+ -1.4685138788754898e-28
+ },
+ 0.02962962962962963,
+ 0.03796296296296296
+ },
+ {
+ {
+ 1.1901434626227093e-10,
+ 1.7361780173369773e-10,
+ 7.639416392753658e-11,
+ 2.219331080562664e-11,
+ 4.468985012784936e-12,
+ 6.345623163747038e-13,
+ 6.256832040916454e-14,
+ 3.9794258615342e-15,
+ 1.2126532982344795e-16,
+ -2.510288446235168e-18,
+ -3.1189177665897616e-19,
+ -3.0550813286427195e-22,
+ 6.384476478410435e-22,
+ 2.6783405454063793e-25,
+ -1.4724057241513977e-24,
+ -5.563678192342752e-26,
+ 1.0097419586828951e-27,
+ 6.679443056687351e-26,
+ 5.4526065768876336e-27
+ },
+ 0.03796296296296296,
+ 0.0462962962962963
+ },
+ {
+ {
+ 3.341667610526653e-08,
+ 5.118389108542411e-08,
+ 2.4371256768154856e-08,
+ 7.57899054003236e-09,
+ 1.5635438033324503e-09,
+ 2.0715013642702e-10,
+ 1.5165995758982126e-11,
+ 1.6314454982752663e-13,
+ -6.017223931292203e-14,
+ -1.9704412673913643e-15,
+ 2.8051398344015177e-16,
+ 7.022929896522875e-18,
+ -1.5199614910962848e-18,
+ 1.1958046052493347e-20,
+ 7.00911492046808e-21,
+ -4.237329623030918e-22,
+ -3.863191954564062e-23,
+ -1.1166938269465874e-23,
+ -1.2818068320304144e-23
+ },
+ 0.0462962962962963,
+ 0.06296296296296297
+ },
+ {
+ {
+ 8.410724206747044e-06,
+ 1.2481631400263709e-05,
+ 5.378159443205515e-06,
+ 1.3704527561658967e-06,
+ 1.9136168235190198e-07,
+ 8.957711663130537e-09,
+ -9.462672897450059e-10,
+ -6.968811539371602e-11,
+ 1.0243849900317855e-11,
+ 2.337729169280951e-13,
+ -1.1494530386099005e-13,
+ 5.3160592525426036e-15,
+ 7.530730564512324e-16,
+ -1.1431990843247566e-16,
+ 2.805445086019535e-18,
+ 7.988918627843267e-19,
+ -1.0295338058018748e-19,
+ 7.210533399624742e-21,
+ 5.761312966431838e-22
+ },
+ 0.06296296296296297,
+ 0.0962962962962963
+ },
+ {
+ {
+ 0.0006802593682753608,
+ 0.0009003332567452364,
+ 0.0002880297751978097,
+ 4.118964226458961e-05,
+ 7.986981798077676e-07,
+ -2.628431475282669e-07,
+ 1.4516582903911464e-08,
+ 1.5647152494426528e-09,
+ -4.1929621787396065e-10,
+ 3.8557343395626107e-11,
+ 8.368753107866514e-13,
+ -8.31125296022126e-13,
+ 1.3326079144488354e-13,
+ -8.864161253017153e-15,
+ -8.83270499045497e-16,
+ 3.3879136780332834e-16,
+ -4.8188763160481214e-17,
+ 2.9076523496871995e-18,
+ 3.8719993601362204e-19
+ },
+ 0.0962962962962963,
+ 0.16296296296296295
+ },
+ {
+ {
+ 0.015871052250174933,
+ 0.017373046113870208,
+ 0.003617191914161977,
+ 0.00018958352208271672,
+ -1.4572937633430827e-05,
+ 7.218425887058066e-07,
+ 2.6419947263015497e-08,
+ -1.4409436469961143e-08,
+ 2.6380419456436925e-09,
+ -3.4860393171849517e-10,
+ 3.335912880024321e-11,
+ -1.2239621615490678e-12,
+ -4.035014645542914e-13,
+ 1.3487363894996995e-13,
+ -2.72259564068969e-14,
+ 4.280375966864147e-15,
+ -5.359753439682091e-16,
+ 5.147249813874932e-17,
+ -1.531435568635775e-18
+ },
+ 0.16296296296296295,
+ 0.2962962962962963
+ }
+}
+};
+const auto vdW_rhoL = SuperAncillary{
+{
+ {
+ {
+ 0.9316136201036852,
+ -0.03865225088424542,
+ -0.0008661148627486168,
+ -3.8336595966463605e-05,
+ -1.930441992932519e-06,
+ -5.810841478132156e-08,
+ 6.379356029539984e-09,
+ 4.0565692471794534e-10,
+ -3.1201431022198634e-10,
+ -3.4029466744467385e-11,
+ 1.369238750159596e-11,
+ 1.18192261533423e-12,
+ -7.751924102628038e-13,
+ 6.175615574477433e-15,
+ 4.091171845743702e-14,
+ -6.980527267330672e-15,
+ -1.2559397966072083e-15,
+ 1.4641066137244252e-15,
+ -3.8163916471489756e-17
+ },
+ 0.02962962962962963,
+ 0.0962962962962963
+ },
+ {
+ {
+ 0.8455034879915954,
+ -0.04802256898834967,
+ -0.0015470962415359973,
+ -7.972501988821878e-05,
+ -4.017234579128948e-06,
+ -2.921741757144769e-07,
+ -2.6298690877779585e-08,
+ -1.3988705679923719e-09,
+ -1.5143918064008943e-10,
+ -1.6808554548219945e-11,
+ -1.6921186674068167e-13,
+ -1.6256440638073855e-13,
+ -9.825473767932635e-15,
+ 7.077671781985373e-16,
+ -3.608224830031759e-16,
+ -7.632783294297951e-16,
+ -4.163336342344337e-17,
+ 8.257283745649602e-16,
+ 1.3877787807814457e-17
+ },
+ 0.0962962962962963,
+ 0.16296296296296295
+ },
+ {
+ {
+ 0.7327617276279949,
+ -0.06612960981729517,
+ -0.0032780016312522198,
+ -0.00026019391083406673,
+ -2.6595986463442967e-05,
+ -3.184060496402852e-06,
+ -4.0508839448810674e-07,
+ -5.4371095223326726e-08,
+ -7.554792333386295e-09,
+ -1.076694275403689e-09,
+ -1.5675695463901462e-10,
+ -2.3183531483450537e-11,
+ -3.4755739952707643e-12,
+ -5.273004255457181e-13,
+ -8.064382495120981e-14,
+ -1.3183898417423734e-14,
+ -1.9290125052862095e-15,
+ 4.0245584642661925e-16,
+ -5.898059818321144e-17
+ },
+ 0.16296296296296295,
+ 0.22962962962962963
+ },
+ {
+ {
+ 0.6166811517612045,
+ -0.04839066994648989,
+ -0.0021672975061474767,
+ -0.00017570976987404258,
+ -1.8519040533800102e-05,
+ -2.208561613849247e-06,
+ -2.82949510460595e-07,
+ -3.8035669329417043e-08,
+ -5.291587154565569e-09,
+ -7.554387740360546e-10,
+ -1.1004187144836308e-10,
+ -1.6289976312311438e-11,
+ -2.4432955658681976e-12,
+ -3.709324514211687e-13,
+ -5.671157987663378e-14,
+ -9.346690088563037e-15,
+ -1.3600232051658168e-15,
+ 3.677613769070831e-16,
+ -3.122502256758253e-17
+ },
+ 0.22962962962962963,
+ 0.26296296296296295
+ },
+ {
+ {
+ 0.5328306974405083,
+ -0.034453741516764766,
+ -0.0014682721939933072,
+ -0.00012182552205808328,
+ -1.2945521315733954e-05,
+ -1.5482578362285837e-06,
+ -1.9873352891802698e-07,
+ -2.6746483347550587e-08,
+ -3.724136381222376e-09,
+ -5.319946913551199e-10,
+ -7.753041264546567e-11,
+ -1.1481385286948864e-11,
+ -1.7225665338571616e-12,
+ -2.6155466681387907e-13,
+ -4.00304789316408e-14,
+ -6.696032617270475e-15,
+ -9.43689570931383e-16,
+ 3.885780586188048e-16,
+ -1.734723475976807e-17
+ },
+ 0.26296296296296295,
+ 0.2796296296296296
+ },
+ {
+ {
+ 0.4734609830190833,
+ -0.02424735785371843,
+ -0.0010133644361935874,
+ -8.529016931251368e-05,
+ -9.098505499984672e-06,
+ -1.089985510512731e-06,
+ -1.4004471942871688e-07,
+ -1.8859509249430362e-08,
+ -2.627095759683007e-09,
+ -3.7540060296437083e-10,
+ -5.472236552783727e-11,
+ -8.105231763533283e-12,
+ -1.2161383011743965e-12,
+ -1.8476886687324168e-13,
+ -2.827946210537391e-14,
+ -4.829470157119431e-15,
+ -7.181755190543981e-16,
+ 4.2674197509029455e-16,
+ 6.938893903907228e-18
+ },
+ 0.2796296296296296,
+ 0.287962962962963
+ },
+ {
+ {
+ 0.4317586705206012,
+ -0.016998875614382822,
+ -0.0007071969216258488,
+ -6.0002743216675675e-05,
+ -6.413721659864063e-06,
+ -7.690254281537967e-07,
+ -9.885537948645107e-08,
+ -1.3316815754282896e-08,
+ -1.855412701950998e-09,
+ -2.6517297732620015e-10,
+ -3.8659075940472576e-11,
+ -5.726488727653134e-12,
+ -8.592571099086399e-13,
+ -1.30593452718486e-13,
+ -1.9970136655445003e-14,
+ -3.4555691641457997e-15,
+ -4.891920202254596e-16,
+ 3.5041414214731503e-16,
+ -6.938893903907228e-18
+ },
+ 0.287962962962963,
+ 0.29212962962962963
+ },
+ {
+ {
+ 0.4025301670915846,
+ -0.011913454752168377,
+ -0.0004965958130950694,
+ -4.231862747736473e-05,
+ -4.528099139627234e-06,
+ -5.431755606445654e-07,
+ -6.984058851383645e-08,
+ -9.409722008524302e-09,
+ -1.311186739044734e-09,
+ -1.8740799190286594e-10,
+ -2.732347334499785e-11,
+ -4.0475123253003176e-12,
+ -6.073752611968075e-13,
+ -9.242259735309233e-14,
+ -1.4089424071883627e-14,
+ -2.5500435096859064e-15,
+ -3.0878077872387166e-16,
+ 3.9898639947466563e-16,
+ -3.122502256758253e-17
+ },
+ 0.29212962962962963,
+ 0.29421296296296295
+ },
+ {
+ {
+ 0.3820369525637211,
+ -0.008358544107590068,
+ -0.00034987653550601003,
+ -2.988469717726469e-05,
+ -3.1993345159762876e-06,
+ -3.8386783924454493e-07,
+ -4.936325082721682e-08,
+ -6.651310394817367e-09,
+ -9.268700876252645e-10,
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+}
+};
+const auto vdW_rhoV = SuperAncillary{
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+ },
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+ },
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+ {
+ {
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+ 4.787836793695988e-16,
+ -2.6020852139652106e-16,
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+ },
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+ {
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+ 1.4981339496820262e-06
+ },
+ 0.29629527904369213,
+ 0.2962962962962963
+ }
+}
+};
+
+const auto SRK_p = SuperAncillary{
+{
+ {
+ {
+ 2.9225473692726744e-13,
+ 4.846211782171669e-13,
+ 2.824570002653489e-13,
+ 1.1955110559200177e-13,
+ 3.771710795961595e-14,
+ 9.009392578047045e-15,
+ 1.6354246747926244e-15,
+ 2.2297564454973646e-16,
+ 2.1977303354380907e-17,
+ 1.4079420760456038e-18,
+ 3.645901247485968e-20,
+ -2.3224668904548756e-21,
+ -2.1119277731077838e-22,
+ 1.3269831236005753e-24,
+ 7.111685153229056e-25,
+ 2.0749322108366765e-27,
+ -2.355803670950289e-27,
+ 1.89511506527704e-29,
+ -1.203321029253145e-29
+ },
+ 0.020267685653535945,
+ 0.02596797224359293
+ },
+ {
+ {
+ 4.42411833611544e-11,
+ 6.486786260066829e-11,
+ 2.8834316573742172e-11,
+ 8.49036232570771e-12,
+ 1.7382606171711586e-12,
+ 2.519225194793423e-13,
+ 2.5510836572731127e-14,
+ 1.688802065855514e-15,
+ 5.658115744876586e-17,
+ -7.526264008617426e-19,
+ -1.3472892665001768e-19,
+ -9.922698129701787e-22,
+ 2.6795301476514526e-22,
+ 2.2940832430296035e-24,
+ -5.789860391087721e-25,
+ 1.1649897848303902e-26,
+ 2.589988124021626e-26,
+ 5.472801416061292e-26,
+ 2.268132874691453e-26
+ },
+ 0.02596797224359293,
+ 0.03166825883364991
+ },
+ {
+ {
+ 1.3403609277725988e-08,
+ 2.0613817317201788e-08,
+ 9.908855672700315e-09,
+ 3.1242347660239074e-09,
+ 6.566525761190694e-10,
+ 8.934527720041564e-11,
+ 6.864947922093292e-12,
+ 1.0961157691701013e-13,
+ -2.552558822185046e-14,
+ -1.0755067059569204e-15,
+ 1.1595758568473605e-16,
+ 4.364935105515505e-18,
+ -6.518267188981206e-19,
+ -2.420947626615306e-21,
+ 3.3222352209999887e-21,
+ -1.4160136552428753e-22,
+ -1.0359144702519558e-23,
+ 3.0017608947725106e-24,
+ -1.1502980393315541e-24
+ },
+ 0.03166825883364991,
+ 0.04306883201376388
+ },
+ {
+ {
+ 3.6266120105336493e-06,
+ 5.40530078063072e-06,
+ 2.3535707621866956e-06,
+ 6.09797026711632e-07,
+ 8.755959081374292e-08,
+ 4.4744907993962915e-09,
+ -4.067655714209484e-10,
+ -3.591728379118743e-11,
+ 4.465366516258063e-12,
+ 1.6493814952480902e-13,
+ -5.3226243319885286e-14,
+ 1.7922687946152793e-15,
+ 4.005718486965302e-16,
+ -4.988684915276682e-17,
+ 4.789814152406683e-19,
+ 4.147268524381617e-19,
+ -4.591183271914325e-20,
+ 4.350970022028926e-22,
+ -1.0629270871306406e-21
+ },
+ 0.04306883201376388,
+ 0.06586997837399182
+ },
+ {
+ {
+ 0.0003094297409003984,
+ 0.0004117661948641284,
+ 0.0001333784156235523,
+ 1.953127675250332e-05,
+ 4.4650824621707415e-07,
+ -1.245752753612688e-07,
+ 6.1713045177982556e-09,
+ 8.457787641085228e-10,
+ -2.019178315130611e-10,
+ 1.671511339141844e-11,
+ 7.461694230598466e-13,
+ -4.260132318823111e-13,
+ 6.171897036311516e-14,
+ -3.212145765269425e-15,
+ -5.836180885150665e-16,
+ 1.719715110942645e-16,
+ -2.147440279526465e-17,
+ 8.273394312306379e-19,
+ 2.34734005507848e-19
+ },
+ 0.06586997837399182,
+ 0.1114722710944477
+ },
+ {
+ {
+ 0.0074771598568592074,
+ 0.008244590094104293,
+ 0.0017465545422224592,
+ 9.786738241774412e-05,
+ -6.516977077872878e-06,
+ 3.2958650511163794e-07,
+ 1.5363696321735632e-08,
+ -7.20353161771562e-09,
+ 1.2861343701874766e-09,
+ -1.6587511786082245e-10,
+ 1.5108394000934097e-11,
+ -3.6747905743763146e-13,
+ -2.33340277167645e-13,
+ 7.039936125372015e-14,
+ -1.3651690997269761e-14,
+ 2.071300487897776e-15,
+ -2.45029690981724e-16,
+ 2.15485181781494e-17,
+ 1.4026865606531214e-18
+ },
+ 0.1114722710944477,
+ 0.20267685653535944
+ }
+}
+};
+const auto SRK_rhoL = SuperAncillary{
+{
+ {
+ {
+ 0.9087646203247287,
+ -0.050607640245558645,
+ -0.0008181930140446145,
+ -3.676466126572436e-05,
+ -1.8153449552124612e-06,
+ -4.2148973304623194e-08,
+ 8.967883102783958e-09,
+ 5.813281384048352e-10,
+ -3.659740635542086e-10,
+ -4.441783746367278e-11,
+ 1.5951594212193498e-11,
+ 1.7195689316906737e-12,
+ -9.141229440068344e-13,
+ -1.4432899320127035e-14,
+ 5.0730253331465747e-14,
+ -6.987466161234579e-15,
+ -1.8318679906315083e-15,
+ 1.5126788710517758e-15,
+ -1.734723475976807e-17
+ },
+ 0.020267685653535945,
+ 0.06586997837399182
+ },
+ {
+ {
+ 0.7992363370107459,
+ -0.059445681918569984,
+ -0.0014502328603496623,
+ -7.138164945971748e-05,
+ -3.2189087307149533e-06,
+ -2.486464586864967e-07,
+ -2.4319133658246006e-08,
+ -1.044768556390796e-09,
+ -1.3343107174712543e-10,
+ -1.679712618996021e-11,
+ 2.2661039711380226e-13,
+ -1.6726897644758765e-13,
+ -1.0783041126671833e-14,
+ 1.4363510381087963e-15,
+ -4.0245584642661925e-16,
+ -7.28583859910259e-16,
+ -4.85722573273506e-17,
+ 7.632783294297951e-16,
+ 1.734723475976807e-17
+ },
+ 0.06586997837399182,
+ 0.1114722710944477
+ },
+ {
+ {
+ 0.6649628598972782,
+ -0.0760521559973085,
+ -0.002952854145734922,
+ -0.0002237665443423284,
+ -2.2837440018151633e-05,
+ -2.7674939431024392e-06,
+ -3.5249351108129767e-07,
+ -4.743986068561634e-08,
+ -6.602545343792343e-09,
+ -9.417646246179245e-10,
+ -1.37257025190074e-10,
+ -2.031076695718781e-11,
+ -3.0466879019641624e-12,
+ -4.624911564832246e-13,
+ -7.074202335033419e-14,
+ -1.1532441668293814e-14,
+ -1.7277845820728999e-15,
+ 3.885780586188048e-16,
+ -2.42861286636753e-17
+ },
+ 0.1114722710944477,
+ 0.15707456381490356
+ },
+ {
+ {
+ 0.5358548459176075,
+ -0.051616853474821534,
+ -0.0019014483430589563,
+ -0.0001522452155350712,
+ -1.6138121186740073e-05,
+ -1.9310179919518333e-06,
+ -2.4780931559553743e-07,
+ -3.3348723178783235e-08,
+ -4.64304821673478e-09,
+ -6.632207977252946e-10,
+ -9.664995193059411e-11,
+ -1.4312308282971031e-11,
+ -2.1472545963518996e-12,
+ -3.260794412263124e-13,
+ -4.987676938128516e-14,
+ -8.229528170033973e-15,
+ -1.2004286453759505e-15,
+ 3.469446951953614e-16,
+ -2.0816681711721685e-17
+ },
+ 0.15707456381490356,
+ 0.1798757101751315
+ },
+ {
+ {
+ 0.4485732937583308,
+ -0.03477837295500611,
+ -0.00128197185101675,
+ -0.00010638749439246392,
+ -1.1344133512683485e-05,
+ -1.3588779068512968e-06,
+ -1.7457610832632975e-07,
+ -2.350823218033593e-08,
+ -3.2744967258524493e-09,
+ -4.678942372438044e-10,
+ -6.820332146273422e-11,
+ -1.0101888076041732e-11,
+ -1.5157701482859665e-12,
+ -2.302880108828731e-13,
+ -3.522182545623309e-14,
+ -5.863365348801608e-15,
+ -8.500145032286355e-16,
+ 3.0878077872387166e-16,
+ -1.9081958235744878e-17
+ },
+ 0.1798757101751315,
+ 0.19127628335524546
+ },
+ {
+ {
+ 0.3896887959074917,
+ -0.02352363480040463,
+ -0.0008864377996999455,
+ -7.48085471366268e-05,
+ -7.994798847377887e-06,
+ -9.585173595394458e-07,
+ -1.2320694868853121e-07,
+ -1.6596597669088498e-08,
+ -2.312318735792074e-09,
+ -3.3046667832770105e-10,
+ -4.817745855034694e-11,
+ -7.136409518881948e-12,
+ -1.0708690878491467e-12,
+ -1.627031842588167e-13,
+ -2.490022077417109e-14,
+ -4.173744683200198e-15,
+ -5.93275428784068e-16,
+ 3.0184188481996443e-16,
+ -1.214306433183765e-17
+ },
+ 0.19127628335524546,
+ 0.19697656994530244
+ },
+ {
+ {
+ 0.3497350745917645,
+ -0.016032294782450524,
+ -0.0006202549276113981,
+ -5.274770800074019e-05,
+ -5.643402364315098e-06,
+ -6.769284142359167e-07,
+ -8.70356488269497e-08,
+ -1.17262048994482e-08,
+ -1.6339517863728226e-09,
+ -2.3353845593487854e-10,
+ -3.404898932246603e-11,
+ -5.04390973432578e-12,
+ -7.568771998034407e-13,
+ -1.1509196373715724e-13,
+ -1.7600504387260685e-14,
+ -3.084338340286763e-15,
+ -4.440892098500626e-16,
+ 2.8449465006019636e-16,
+ -3.469446951953614e-18
+ },
+ 0.19697656994530244,
+ 0.19982671324033094
+ },
+ {
+ {
+ 0.3224124351709759,
+ -0.011013634884520482,
+ -0.00043639529901024973,
+ -3.724427437728703e-05,
+ -3.986980578418037e-06,
+ -4.783591501592022e-07,
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+ {
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+ 0.20267546486382865,
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+ },
+ {
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+ -1.3200081928170515e-06
+ },
+ 0.20267616069959404,
+ 0.20267685653535944
+ }
+}
+};
+const auto SRK_rhoV = SuperAncillary{
+{
+ {
+ {
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+ -8.328903877850174e-25,
+ -5.167748904012326e-26,
+ 3.2366962941218114e-27,
+ -1.163964265653603e-27
+ },
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+ 0.02596797224359293
+ },
+ {
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+ 8.243533350687156e-25,
+ 1.8130926610110065e-24,
+ 6.625926732877158e-25
+ },
+ 0.02596797224359293,
+ 0.03166825883364991
+ },
+ {
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+ },
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+ },
+ {
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+ 8.536503921547246e-20,
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+ },
+ 0.04306883201376388,
+ 0.06586997837399182
+ },
+ {
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+ -6.8516495103400354e-18
+ },
+ 0.06586997837399182,
+ 0.1114722710944477
+ },
+ {
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+ 1.6929274822274909e-15,
+ 2.8888566885876266e-16,
+ 4.003416521902725e-17
+ },
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+ 0.15707456381490356
+ },
+ {
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+ },
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+ 3.274496806517091e-09,
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+ },
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+ },
+ {
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+ 1.7780915628762273e-17
+ },
+ 0.19127628335524546,
+ 0.19697656994530244
+ },
+ {
+ {
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+ },
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+ },
+ {
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+ },
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+ },
+ {
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+ },
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+ },
+ {
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+ },
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+ },
+ {
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+ {
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+ 1.2663481374630692e-16
+ },
+ 0.20263232304637463,
+ 0.20265458979086703
+ },
+ {
+ {
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+ -9.540979117872439e-18
+ },
+ 0.20265458979086703,
+ 0.20266572316311324
+ },
+ {
+ {
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+ -7.806255641895632e-18
+ },
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+ 0.20267128984923632
+ },
+ {
+ {
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+ },
+ 0.20267128984923632,
+ 0.20267407319229788
+ },
+ {
+ {
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+ 0.0003167272897560327,
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+ -6.661338147750939e-16,
+ -7.892991815694472e-17
+ },
+ 0.20267407319229788,
+ 0.20267546486382865
+ },
+ {
+ {
+ 0.2585988724599927,
+ 0.00022414215980744862,
+ 9.597255035097285e-06,
+ 8.217756915021579e-07,
+ 8.802244440969664e-08,
+ 1.0563647474121085e-08,
+ 1.358598076053874e-09,
+ 1.8307183026478047e-10,
+ 2.5511984885762118e-11,
+ 3.646605586937746e-12,
+ 5.308739559062303e-13,
+ 7.936012957898697e-14,
+ 1.395758508770939e-14,
+ 1.1587952819525071e-15,
+ -7.546047120499111e-16,
+ -3.0704605524789486e-16,
+ -6.401129626354418e-16,
+ 4.4374226515486725e-15,
+ 1.3426759704060487e-15
+ },
+ 0.20267546486382865,
+ 0.20267616069959404
+ },
+ {
+ {
+ 0.2592290354916159,
+ 0.00046237072283881325,
+ 9.327071111846566e-05,
+ 4.04856404778442e-05,
+ 2.2898027861355946e-05,
+ 1.4911944355256584e-05,
+ 1.0620804294380476e-05,
+ 8.055933548441543e-06,
+ 6.4069163158222975e-06,
+ 5.29011720291038e-06,
+ 4.504867114601269e-06,
+ 3.9380722249553884e-06,
+ 3.522259974053296e-06,
+ 3.215401816561783e-06,
+ 2.9905059784306187e-06,
+ 2.829948342482e-06,
+ 2.7222590090452553e-06,
+ 2.66026259132697e-06,
+ 1.3200081928118473e-06
+ },
+ 0.20267616069959404,
+ 0.20267685653535944
+ }
+}
+};
+
+const auto PR_p = SuperAncillary{
+{
+ {
+ {
+ 4.2115936784941e-14,
+ 7.082139279778615e-14,
+ 4.281441668412217e-14,
+ 1.9123012372347713e-14,
+ 6.460328562307523e-15,
+ 1.6765603431288853e-15,
+ 3.36292637163962e-16,
+ 5.1860921648633566e-17,
+ 6.0107675456840275e-18,
+ 4.93726813515645e-19,
+ 2.4083621285564296e-20,
+ 9.47616424537102e-23,
+ -7.1051225501406e-23,
+ -3.0677436333050444e-24,
+ 1.4628333292452202e-25,
+ 1.2639227645878215e-26,
+ -3.8533659659909825e-28,
+ -3.5261080979808146e-29,
+ 3.32550323497344e-30
+ },
+ 0.01701444200703503,
+ 0.021799753821513633
+ },
+ {
+ {
+ 8.938956773181632e-12,
+ 1.3439327305351806e-11,
+ 6.288329039800055e-12,
+ 1.9826748553822934e-12,
+ 4.414511850216345e-13,
+ 7.088859014953733e-14,
+ 8.181698505611952e-15,
+ 6.527653757029151e-16,
+ 3.162152136162365e-17,
+ 4.279990806191533e-19,
+ -4.6206272928403434e-20,
+ -2.0797341030133568e-21,
+ 6.177896652744867e-23,
+ 4.7788231227984526e-24,
+ -1.3861706054362575e-25,
+ -1.4215273512082633e-26,
+ -1.669229675447661e-27,
+ 4.487040828897115e-27,
+ 7.7150596530614955e-28
+ },
+ 0.021799753821513633,
+ 0.026585065635992236
+ },
+ {
+ {
+ 4.085507279084059e-09,
+ 6.410401559266648e-09,
+ 3.231824978266208e-09,
+ 1.0923069013593605e-09,
+ 2.52024445187971e-10,
+ 3.905509723141962e-11,
+ 3.73471874979177e-12,
+ 1.5022634999916855e-13,
+ -8.12601770161866e-15,
+ -9.644616840775853e-16,
+ 2.3559108130823366e-17,
+ 4.723565049544365e-18,
+ -1.6713754821230258e-19,
+ -1.9677138009092646e-20,
+ 1.4426017766021298e-21,
+ 3.847561149043651e-23,
+ -1.0404785039052024e-23,
+ 1.3764802380765226e-24,
+ 4.620579202932928e-25
+ },
+ 0.026585065635992236,
+ 0.03615568926494944
+ },
+ {
+ {
+ 1.6349625391332918e-06,
+ 2.489669257624972e-06,
+ 1.1427314989998866e-06,
+ 3.2189532774728283e-07,
+ 5.2973211090187104e-08,
+ 3.881322341579814e-09,
+ -1.402363237723129e-10,
+ -3.26068965484856e-11,
+ 1.5764214067874998e-12,
+ 2.669115963311214e-13,
+ -2.6973487736840458e-14,
+ -1.1725895938982276e-15,
+ 3.409623244140794e-16,
+ -1.3374770488526952e-17,
+ -2.1340688015269687e-18,
+ 3.0499875924358835e-19,
+ -9.006032316747658e-21,
+ 5.945360652724886e-23,
+ 7.708806321111372e-22
+ },
+ 0.03615568926494944,
+ 0.05529693652286385
+ },
+ {
+ {
+ 0.00018641763706717313,
+ 0.0002549265195801485,
+ 8.796517801636943e-05,
+ 1.4493063101704085e-05,
+ 5.93659937733161e-07,
+ -8.865727397666071e-08,
+ 1.5453090824947498e-09,
+ 1.0034143700587606e-09,
+ -1.473603817532662e-10,
+ 4.333381441536222e-12,
+ 1.903659250210749e-12,
+ -3.854457196096114e-13,
+ 2.9156300395036635e-14,
+ 2.2880752244019054e-15,
+ -9.628463327642823e-16,
+ 1.2770440460045229e-16,
+ -4.453540417985501e-18,
+ -1.6186270226437646e-18,
+ 3.6149778002037437e-19
+ },
+ 0.05529693652286385,
+ 0.09357943103869266
+ },
+ {
+ {
+ 0.005448712641404622,
+ 0.0062362159058999755,
+ 0.001443947803998351,
+ 0.00010960884095892343,
+ -2.254571049831034e-06,
+ 3.108042103893788e-07,
+ 3.183233642737454e-08,
+ -6.3983755658182065e-09,
+ 1.1291747205506315e-09,
+ -1.183401464725808e-10,
+ 7.412891426996499e-12,
+ 7.92415429334923e-13,
+ -3.6369037393225306e-13,
+ 7.890138331101762e-14,
+ -1.258085161656014e-14,
+ 1.5166023276634577e-15,
+ -1.0518116325825e-16,
+ -6.600080725005508e-18,
+ 5.5294310796760726e-18
+ },
+ 0.09357943103869266,
+ 0.1701444200703503
+ }
+}
+};
+const auto PR_rhoL = SuperAncillary{
+{
+ {
+ {
+ 0.9207205305399191,
+ -0.045064618991104796,
+ -0.0010750229061558397,
+ -4.150471723450566e-05,
+ -2.0449656082804912e-06,
+ -8.411570305566496e-08,
+ 2.630701059769258e-09,
+ 7.618859571012493e-10,
+ -1.2385135972348138e-10,
+ -4.380963647410141e-11,
+ 3.6138314563061158e-12,
+ 2.0083795737591004e-12,
+ -2.442004931602071e-13,
+ -8.769374115757955e-14,
+ 2.0539125955565396e-14,
+ 1.4155343563970746e-15,
+ -1.4502288259166107e-15,
+ 9.645062526431047e-16,
+ 4.85722573273506e-17
+ },
+ 0.01701444200703503,
+ 0.05529693652286385
+ },
+ {
+ {
+ 0.8199443180127295,
+ -0.056330799734005496,
+ -0.0018219491199177318,
+ -8.821642822268161e-05,
+ -4.3808005871781575e-06,
+ -2.7804292488525784e-07,
+ -2.5617864357618814e-08,
+ -1.4936050521385802e-09,
+ -1.1656688808647786e-10,
+ -1.80864212495635e-11,
+ -3.4572344986827375e-13,
+ -7.897849041427207e-14,
+ -1.9761969838327786e-14,
+ 1.0269562977782698e-15,
+ -1.5265566588595902e-16,
+ -7.91033905045424e-16,
+ -2.7755575615628914e-17,
+ 8.049116928532385e-16,
+ 2.0816681711721685e-17
+ },
+ 0.05529693652286385,
+ 0.09357943103869266
+ },
+ {
+ {
+ 0.6880146598953387,
+ -0.07711229066058617,
+ -0.0036751053290779087,
+ -0.00027023163542316125,
+ -2.612667202559621e-05,
+ -3.0579327836427472e-06,
+ -3.869841956188891e-07,
+ -5.180305783641925e-08,
+ -7.196452149471622e-09,
+ -1.0250969587066727e-09,
+ -1.492256387902735e-10,
+ -2.2068007143882795e-11,
+ -3.3078817462950383e-12,
+ -5.018416238122825e-13,
+ -7.670947210769441e-14,
+ -1.2490009027033011e-14,
+ -1.887379141862766e-15,
+ 3.5388358909926865e-16,
+ -2.7755575615628914e-17
+ },
+ 0.09357943103869266,
+ 0.13186192555452148
+ },
+ {
+ {
+ 0.5539049274549523,
+ -0.05513150079759916,
+ -0.00226486529446273,
+ -0.00017169038790523783,
+ -1.771968913242411e-05,
+ -2.1044071880221837e-06,
+ -2.6937613983174513e-07,
+ -3.620174487267702e-08,
+ -5.035860249635871e-09,
+ -7.188804967972473e-10,
+ -1.0471176703497065e-10,
+ -1.5500455086137066e-11,
+ -2.3248417080345973e-12,
+ -3.5293989952833726e-13,
+ -5.399847236020605e-14,
+ -8.854028621385623e-15,
+ -1.2975731600306517e-15,
+ 2.8449465006019636e-16,
+ -4.5102810375396984e-17
+ },
+ 0.13186192555452148,
+ 0.1510031728124359
+ },
+ {
+ {
+ 0.459674826377972,
+ -0.03799561202969537,
+ -0.0014593552334729865,
+ -0.00011667442436243125,
+ -1.2328894690105674e-05,
+ -1.4734787574105512e-06,
+ -1.89107481913392e-07,
+ -2.5449463390836424e-08,
+ -3.5434242970366903e-09,
+ -5.061691760177567e-10,
+ -7.376567759398434e-11,
+ -1.0923841692322966e-11,
+ -1.6389077595047041e-12,
+ -2.489328188026718e-13,
+ -3.807371085073896e-14,
+ -6.283168429987995e-15,
+ -9.055256544598933e-16,
+ 3.0531133177191805e-16,
+ -2.2551405187698492e-17
+ },
+ 0.1510031728124359,
+ 0.16057379644139308
+ },
+ {
+ {
+ 0.39512265522451157,
+ -0.025874636107352526,
+ -0.000981657847521144,
+ -8.126867623134762e-05,
+ -8.658142312312905e-06,
+ -1.0370940123176353e-06,
+ -1.3324415930673905e-07,
+ -1.794336704219468e-08,
+ -2.4994516144294376e-09,
+ -3.5715819884929445e-10,
+ -5.20629060696276e-11,
+ -7.711369737206653e-12,
+ -1.157088314052146e-12,
+ -1.7580381594939354e-13,
+ -2.6891683324592464e-14,
+ -4.472117121068209e-15,
+ -6.314393452555578e-16,
+ 2.636779683484747e-16,
+ -1.734723475976807e-17
+ },
+ 0.16057379644139308,
+ 0.1653591082558717
+ },
+ {
+ {
+ 0.3511712698170222,
+ -0.01762984199424723,
+ -0.0006775212105428925,
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+ {
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+ {
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+ },
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+ {
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+ -9.107298248878237e-17
+ },
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+ 0.17013507375821263
+ },
+ {
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+ -5.828670879282072e-16
+ },
+ 0.17013507375821263,
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+ },
+ {
+ {
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+ 1.951563910473908e-16
+ },
+ 0.17013974691428146,
+ 0.17014208349231588
+ },
+ {
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+ -2.7955775715182707e-10,
+ -3.895907554896105e-11,
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+ -1.156644224842296e-13,
+ -1.7319479184152442e-14,
+ -6.123573870198129e-16,
+ -6.765421556309548e-17,
+ 1.5838025335668249e-15,
+ 2.5326962749261384e-16,
+ 1.56472057533108e-15,
+ 1.1622647289044608e-16
+ },
+ 0.17014208349231588,
+ 0.1701432517813331
+ },
+ {
+ {
+ 0.25450739757424595,
+ -0.0002430797888991077,
+ -1.0362693722733643e-05,
+ -8.873161782604194e-07,
+ -9.50426266178167e-08,
+ -1.1406137241307124e-08,
+ -1.4669526513660935e-09,
+ -1.976803373771041e-10,
+ -2.754695430096099e-11,
+ -3.937652287566706e-12,
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+ -1.5083420623618338e-14,
+ -2.8484159475539172e-15,
+ 9.280770596475918e-16,
+ -8.326672684688674e-17,
+ 1.0928757898653885e-15,
+ -1.9723805921856297e-15,
+ -1.4632392519864368e-15
+ },
+ 0.1701432517813331,
+ 0.1701438359258417
+ },
+ {
+ {
+ 0.25382485353286033,
+ -0.0005003082472470298,
+ -0.00010070946646463866,
+ -4.371453981542178e-05,
+ -2.472424034292986e-05,
+ -1.6101233343186055e-05,
+ -1.1467857101349344e-05,
+ -8.698427342242881e-06,
+ -6.917894183581727e-06,
+ -5.7120257463023905e-06,
+ -4.864148734601281e-06,
+ -4.252149622345491e-06,
+ -3.803174641357071e-06,
+ -3.471843289028567e-06,
+ -3.2290110822119633e-06,
+ -3.0556483156078673e-06,
+ -2.9393703138338306e-06,
+ -2.8724294233051922e-06,
+ -1.425284251615512e-06
+ },
+ 0.1701438359258417,
+ 0.1701444200703503
+ }
+}
+};
+const auto PR_rhoV = SuperAncillary{
+{
+ {
+ {
+ 1.967544593078315e-12,
+ 3.286395018856467e-12,
+ 1.951259019068106e-12,
+ 8.480414006053818e-13,
+ 2.7638255525455143e-13,
+ 6.855112175816157e-14,
+ 1.2987941190221208e-14,
+ 1.8596645822713178e-15,
+ 1.9425469025161906e-16,
+ 1.3440422453482796e-17,
+ 4.1371292677837237e-19,
+ -2.0472087922962698e-20,
+ -2.3984414514408427e-21,
+ -1.0726839771583605e-23,
+ 8.190099610752978e-24,
+ 1.4834694490433158e-25,
+ -2.890640271333655e-26,
+ -1.2318556073091862e-28,
+ 2.6437933681383566e-28
+ },
+ 0.01701444200703503,
+ 0.021799753821513633
+ },
+ {
+ {
+ 3.4427283919277603e-10,
+ 5.10033605480091e-10,
+ 2.3125713682061785e-10,
+ 6.97923116109859e-11,
+ 1.468781950176213e-11,
+ 2.192555878654968e-12,
+ 2.289969778559488e-13,
+ 1.563184655125417e-14,
+ 5.345224322369889e-16,
+ -8.665670712890633e-18,
+ -1.4805111905363385e-18,
+ -1.2881526260516941e-20,
+ 3.1913825586258806e-21,
+ 4.0303951255023627e-23,
+ -7.672322324660242e-24,
+ -2.068961273341252e-25,
+ -4.90734591919887e-26,
+ 1.348005514841665e-25,
+ 2.4183319910455338e-26
+ },
+ 0.021799753821513633,
+ 0.026585065635992236
+ },
+ {
+ {
+ 1.1651253109754791e-07,
+ 1.799247246805057e-07,
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+ 2.7723805947266338e-08,
+ 5.859084478366607e-09,
+ 7.937371730144063e-10,
+ 5.851825200412916e-11,
+ 3.5459917618408365e-13,
+ -2.840460099622861e-13,
+ -9.001110583611441e-15,
+ 1.453688138264624e-15,
+ 4.153752300772462e-17,
+ -8.493292717205814e-18,
+ 1.0460073661948098e-20,
+ 4.4932489647971677e-20,
+ -2.1592128174018962e-21,
+ -1.6723265540349414e-22,
+ 6.45330124762073e-23,
+ 1.344814730252227e-23
+ },
+ 0.026585065635992236,
+ 0.03615568926494944
+ },
+ {
+ {
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+ 4.5977523083262384e-05,
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+ 2.0013065084957464e-08,
+ -4.62369606718499e-09,
+ -1.6742776075828521e-10,
+ 5.6102600385966035e-11,
+ -2.1810195956609656e-13,
+ -6.246733592709029e-13,
+ 4.045717710917202e-14,
+ 3.97102187587516e-15,
+ -7.21043417103846e-16,
+ 1.9805582453051167e-17,
+ 4.946315069940491e-18,
+ -6.192935810062008e-19,
+ 5.64732747802203e-20,
+ 1.2579762755706445e-20
+ },
+ 0.03615568926494944,
+ 0.05529693652286385
+ },
+ {
+ {
+ 0.0005902854802776641,
+ 0.0006119857879876187,
+ 0.000137226493734894,
+ 1.3534511317666194e-05,
+ 2.5757985750152563e-07,
+ -3.0381140235968494e-08,
+ 1.4660600077037917e-09,
+ 1.4064389556322658e-10,
+ -1.7247649444289924e-11,
+ 4.829482286631236e-13,
+ 7.904912957394129e-14,
+ -9.965950794102972e-15,
+ 3.496086138144762e-16,
+ 3.581424707580633e-17,
+ -5.7462715141731735e-18,
+ 5.929230630780102e-20,
+ 6.776263578034403e-21,
+ 5.166900978251232e-19,
+ 1.1858461261560205e-20
+ },
+ 0.05529693652286385,
+ 0.07443818378077825
+ },
+ {
+ {
+ 0.0034551514866857118,
+ 0.002398865145025046,
+ 0.0003121082643740536,
+ 1.5218984619397858e-05,
+ 9.690936261096291e-08,
+ 1.2913919961681083e-08,
+ 1.4096536882115922e-09,
+ -3.3114702454217944e-11,
+ 2.594155481248396e-12,
+ 1.6231949866250123e-13,
+ -1.3332379904945624e-14,
+ 1.0818033751788803e-15,
+ -1.3362791775883842e-17,
+ -2.2497195079074217e-18,
+ -9.486769009248164e-20,
+ -1.2197274440461925e-18,
+ -2.303929616531697e-19,
+ 3.6591823321385775e-18,
+ 3.9979955110402976e-19
+ },
+ 0.07443818378077825,
+ 0.09357943103869266
+ },
+ {
+ {
+ 0.020288628115803765,
+ 0.016610099415744563,
+ 0.00272192651625002,
+ 0.0002394799179501481,
+ 2.3315294231581688e-05,
+ 3.169727025417485e-06,
+ 3.793923939678003e-07,
+ 5.156601162595916e-08,
+ 7.275292876224738e-09,
+ 1.0148922060279446e-09,
+ 1.5007760583319457e-10,
+ 2.202715483970441e-11,
+ 3.3070396464676688e-12,
+ 5.021763712330374e-13,
+ 7.666279720416891e-14,
+ 1.1847890290378471e-14,
+ 1.843794214528849e-15,
+ 3.1604493327952454e-16,
+ 4.651227319962814e-17
+ },
+ 0.09357943103869266,
+ 0.13186192555452148
+ },
+ {
+ {
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+ 0.021523786193835045,
+ 0.001926244019335927,
+ 0.00016436263238290855,
+ 1.7587241022322224e-05,
+ 2.103887459802955e-06,
+ 2.692872191701126e-07,
+ 3.6202589339100893e-08,
+ 5.035822049290206e-09,
+ 7.188798449749012e-10,
+ 1.0471208969353718e-10,
+ 1.5500948181285112e-11,
+ 2.3252866646061854e-12,
+ 3.5267275211303684e-13,
+ 5.3994569232385103e-14,
+ 8.295447662121092e-15,
+ 1.2962721174236691e-15,
+ 2.658463726934457e-16,
+ 3.230922474006803e-17
+ },
+ 0.13186192555452148,
+ 0.1510031728124359
+ },
+ {
+ {
+ 0.10209461339960167,
+ 0.020078909930632285,
+ 0.0013564703941337276,
+ 0.00011554892995170075,
+ 1.2319437775788929e-05,
+ 1.4734155808103153e-06,
+ 1.8910621422518065e-07,
+ 2.5449462346532892e-08,
+ 3.5434243221901807e-09,
+ 5.06168969585663e-10,
+ 7.376593953722921e-11,
+ 1.0924287516256292e-11,
+ 1.6393041438189648e-12,
+ 2.4869169223951104e-13,
+ 3.807978238290488e-14,
+ 5.776629175002768e-15,
+ 9.063930161978817e-16,
+ 2.411265631607762e-16,
+ 2.0383000842727483e-17
+ },
+ 0.1510031728124359,
+ 0.16057379644139308
+ },
+ {
+ {
+ 0.1393729010835231,
+ 0.016593251298797226,
+ 0.0009532795808090732,
+ 8.111304465426971e-05,
+ 8.657481578122454e-06,
+ 1.037091311451195e-06,
+ 1.332441384432198e-07,
+ 1.794336703699051e-08,
+ 2.4994517905038705e-09,
+ 3.571580193054147e-10,
+ 5.2063129848956e-11,
+ 7.711812959054765e-12,
+ 1.157456075429053e-12,
+ 1.7556355674797075e-13,
+ 2.688300970721258e-14,
+ 3.9968028886505635e-15,
+ 6.323067069935462e-16,
+ 2.2985086056692694e-16,
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+ },
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+ 1.4252842516137773e-06
+ },
+ 0.1701438359258417,
+ 0.1701444200703503
+ }
+}
+};
+
+double supercubic(int EOS, int prop, double Ttilde){
+ switch(EOS){
+ case 0:{
+ switch(prop){
+ case 100:
+ return vdW_p.y(Ttilde);
+ case 101:
+ return vdW_rhoL.y(Ttilde);
+ case 102:
+ return vdW_rhoV.y(Ttilde);
+ default:
+ return -2;
+ }
+ }
+ case 1:{
+ switch(prop){
+ case 100:
+ return SRK_p.y(Ttilde);
+ case 101:
+ return SRK_rhoL.y(Ttilde);
+ case 102:
+ return SRK_rhoV.y(Ttilde);
+ default:
+ return -2;
+ }
+ }
+ case 2:{
+ switch(prop){
+ case 100:
+ return PR_p.y(Ttilde);
+ case 101:
+ return PR_rhoL.y(Ttilde);
+ case 102:
+ return PR_rhoV.y(Ttilde);
+ default:
+ return -2;
+ }
+ }
+ default:
+ return -1;
+ }
+}
+
+const int VDW_CODE = 0, SRK_CODE = 1, PR_CODE = 2;
+const int P_CODE = 100, RHOL_CODE = 101, RHOV_CODE = 102;
+
+}; // namespace CubicSuperAncillary
\ No newline at end of file
diff --git a/include/teqp/models/eos.hpp b/include/teqp/models/eos.hpp
index c9e77c2c9e05886990254b8c0f9846019a64d9d0..dd8e17dda7c812ccecd1e41c8f326bcdcc4a2339 100644
--- a/include/teqp/models/eos.hpp
+++ b/include/teqp/models/eos.hpp
@@ -45,6 +45,20 @@ protected:
template<typename TType, typename IndexType>
auto get_bi(TType T, IndexType i) const { return bi[i]; }
+
+
+public:
+ vdWEOS(const std::valarray<NumType>& Tc_K, const std::valarray<NumType>& pc_Pa)
+ {
+ ai.resize(Tc_K.size());
+ bi.resize(Tc_K.size());
+ for (auto i = 0; i < Tc_K.size(); ++i) {
+ ai[i] = 27.0 / 64.0 * pow(R * Tc_K[i], 2) / pc_Pa[i];
+ bi[i] = 1.0 / 8.0 * R * Tc_K[i] / pc_Pa[i];
+ }
+ k = std::valarray<std::valarray<NumType>>(std::valarray<NumType>(0.0, Tc_K.size()), Tc_K.size());
+ };
+
template<typename TType, typename CompType>
auto a(TType T, const CompType& molefracs) const {
typename CompType::value_type a_ = 0.0;
@@ -67,18 +81,6 @@ protected:
return forceeval(b_);
}
-public:
- vdWEOS(const std::valarray<NumType>& Tc_K, const std::valarray<NumType>& pc_Pa)
- {
- ai.resize(Tc_K.size());
- bi.resize(Tc_K.size());
- for (auto i = 0; i < Tc_K.size(); ++i) {
- ai[i] = 27.0 / 64.0 * pow(R * Tc_K[i], 2) / pc_Pa[i];
- bi[i] = 1.0 / 8.0 * R * Tc_K[i] / pc_Pa[i];
- }
- k = std::valarray<std::valarray<NumType>>(std::valarray<NumType>(0.0, Tc_K.size()), Tc_K.size());
- };
-
const NumType R = get_R_gas<double>();
template<typename TType, typename RhoType, typename MoleFracType>
diff --git a/src/tests/catch_tests.cxx b/src/tests/catch_tests.cxx
index 63d213d16b4edf37a0987a5a3e249bb36742890c..af9ea154b2001821e9ec5694d602e1519ccb2235 100644
--- a/src/tests/catch_tests.cxx
+++ b/src/tests/catch_tests.cxx
@@ -3,6 +3,7 @@
#include "teqp/core.hpp"
#include "teqp/models/pcsaft.hpp"
+#include "teqp/models/cubicsuperancillary.hpp"
#include "teqp/algorithms/VLE.hpp"
auto build_vdW_argon() {
@@ -232,6 +233,39 @@ TEST_CASE("Test psir gradient", "") {
CHECK(err1 < 1e-12);
}
+TEST_CASE("Test extrapolate from critical point", "") {
+ std::valarray<double> Tc_K = { 150.687};
+ std::valarray<double> pc_Pa = { 4863000.0};
+ vdWEOS<double> model(Tc_K, pc_Pa);
+ const auto Zc = 3.0 / 8.0;
+ auto stepper = [&model, &pc_Pa, &Tc_K, &Zc](double step) {
+ auto rhoc_molm3 = pc_Pa[0] / (model.R * Tc_K[0]) / Zc;
+ auto T = Tc_K[0] - step;
+ auto rhovec = extrapolate_from_critical(model, Tc_K[0], rhoc_molm3, T);
+ auto z = (Eigen::ArrayXd(1) << 1.0).finished();
+
+ auto b = model.b(z), a = model.a(T, z), R = model.R;
+ auto Ttilde = R*T*b/a;
+ using namespace CubicSuperAncillary;
+ auto SArhoL = supercubic(VDW_CODE, RHOL_CODE, Ttilde) / b;
+ auto SArhoV = supercubic(VDW_CODE, RHOV_CODE, Ttilde) / b;
+
+ auto resid = IsothermPureVLEResiduals(model, T);
+ auto rhosoln = do_pure_VLE_T(resid, rhovec[0], rhovec[1], 20);
+ auto r0 = resid.call(rhosoln);
+
+ auto errrhoL = SArhoL - rhosoln[0], errrhoV = SArhoV - rhosoln[1];
+ if (std::abs(errrhoL)/SArhoL > 1e-10) {
+ throw std::range_error("rhoL error > 1e-10"); }
+ if (std::abs(errrhoV)/SArhoV > 1e-10) {
+ throw std::range_error("rhoV error > 1e-10"); }
+ };
+ CHECK_NOTHROW(stepper(0.01));
+ CHECK_NOTHROW(stepper(0.1));
+ CHECK_NOTHROW(stepper(1.0));
+ CHECK_NOTHROW(stepper(10.0));
+}
+
TEST_CASE("Test pure VLE", "") {
const auto model = build_vdW_argon();
double T = 100.0;
@@ -244,5 +278,31 @@ TEST_CASE("Test pure VLE", "") {
auto r1 = resid.call(rhovec1);
CHECK((r0.cwiseAbs() > r1.cwiseAbs()).eval().all());
- do_pure_VLE_T(resid, T, 22834.056386882046, 1025.106554560764, 20);
+ auto rhosoln = do_pure_VLE_T(resid, 22834.056386882046, 1025.106554560764, 20);
+ auto rsoln = resid.call(rhosoln);
+ CHECK((rsoln.cwiseAbs() < 1e-8).all());
+}
+
+TEST_CASE("Test pure VLE with non-unity R0/Rr", "") {
+ const auto model = build_vdW_argon();
+ double T = 100.0;
+
+ auto residnormal = IsothermPureVLEResiduals(model, T);
+ auto soln0 = do_pure_VLE_T(residnormal, 22834.056386882046, 1025.106554560764, 20);
+ auto r0 = residnormal.call(soln0);
+
+ double Omega_b = 1.0 / 8, Omega_a = 27.0 / 64;
+ double Tcrit = 150.687, pcrit = 4863000.0; // Argon
+ double Rr = 7.9144;
+ double b = Omega_b * Rr * Tcrit / pcrit;
+ double ba = Omega_b / Omega_a / Tcrit / Rr; // b/a
+ double a = b / ba;
+ auto vdW = vdWEOS1(a, b);
+
+ auto residspecial = IsothermPureVLEResiduals(vdW, T);
+ residspecial.Rr = Rr;
+ auto solnspecial = do_pure_VLE_T(residspecial, 22834.056386882046, 1025.106554560764, 20);
+ auto r1 = residspecial.call(solnspecial);
+
+ auto rr = 0;
}
\ No newline at end of file