johnson.hpp

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#pragma once
 
namespace teqp::mie::lennardjones::Kolafa {
class LJ126KolafaNezbeda1994{
private:
    
    const double MY_PI = EIGEN_PI;
    
    const std::vector<std::tuple<int, double>> c_dhBH  {
        {-2,  0.011117524},
        {-1, -0.076383859},
        { 0,  1.080142248},
        { 1,  0.000693129}
    };
    const double c_ln_dhBH = -0.063920968;
    
    const std::vector<std::tuple<int, double>> c_Delta_B2_hBH  {
        {-7, -0.58544978},
        {-6, 0.43102052},
        {-5, 0.87361369},
        {-4, -4.13749995},
        {-3, 2.90616279},
        {-2, -7.02181962},
        { 0, 0.02459877}
    };
    
    const std::vector<std::tuple<int, int, double>> c_Cij = {
        { 0, 2,    2.01546797},
        { 0, 3,  -28.17881636},
        { 0, 4,   28.28313847},
        { 0, 5,  -10.42402873},
        {-1, 2,  -19.58371655},
        {-1, 3,   75.62340289},
        {-1, 4, -120.70586598},
        {-1, 5,  93.92740328},
        {-1, 6, -27.37737354},
        {-2, 2, 29.34470520},
        {-2, 3, -112.3535693},
        {-2,  4, 170.64908980 },
        {-2, 5, -123.06669187},
        {-2, 6, 34.42288969 },
        {-4, 2, -13.37031968},
        {-4, 3, 65.38059570},
        {-4, 4, -115.09233113},
        {-4, 5, 88.91973082},
        {-4, 6, -25.62099890}
    };
    
    const double gamma = 1.92907278;
    
    // Form of Eq. 29
    template<typename TTYPE>
    auto get_dhBH(const TTYPE& Tstar) const {
        TTYPE summer = c_ln_dhBH*log(Tstar);
        for (auto [i, C_i] : c_dhBH){
            summer += C_i*pow(Tstar, i/2.0);
        }
        return forceeval(summer);
    }
    
    template<typename TTYPE>
    auto get_d_dhBH_d1T(const TTYPE& Tstar) const {
        TTYPE summer = c_ln_dhBH;
        for (auto [i, C_i] : c_dhBH){
            summer += (i/2.0)*C_i*pow(Tstar, i/2.0);
        }
        return forceeval(-Tstar*summer);
    }
    
    // Form of Eq. 29
    template<typename TTYPE>
    auto get_DeltaB2hBH(const TTYPE& Tstar) const {
        TTYPE summer = 0.0;
        for (auto [i, C_i] : c_Delta_B2_hBH){
            summer += C_i*pow(Tstar, i/2.0);
        }
        return forceeval(summer);
    }
    
    template<typename TTYPE>
    auto get_d_DeltaB2hBH_d1T(const TTYPE& Tstar) const {
        TTYPE summer = 0.0;
        for (auto [i, C_i] : c_Delta_B2_hBH){
            summer += (i/2.0)*C_i*pow(Tstar, i/2.0);
        }
        return forceeval(-Tstar*summer);
    }
    
    //  Eq. 5 from K-N
    template<typename TTYPE, typename RHOTYPE>
    auto get_ahs(const TTYPE& Tstar, const RHOTYPE& rhostar) const {
        auto zeta = MY_PI/6.0*rhostar*pow(get_dhBH(Tstar), 3);
        return forceeval(Tstar*(5.0/3.0*log(1.0-zeta) + zeta*(34.0-33.0*zeta+4.0*POW2(zeta))/(6.0*POW2(1.0-zeta))));
    }
    
    // Eq. 4 from K-N
    template<typename TTYPE, typename RHOTYPE>
    auto get_zhs(const TTYPE& Tstar, const RHOTYPE& rhostar) const {
        std::common_type_t<TTYPE, RHOTYPE> zeta = MY_PI/6.0*rhostar*POW3(get_dhBH(Tstar));
        return forceeval((1.0+zeta+zeta**zeta-2.0/3.0*POW3(zeta)*(1+zeta))/POW3(1.0-zeta));
    }
    
    // Eq. 30 from K-N
    template<typename TTYPE, typename RHOTYPE>
    auto get_a(const TTYPE& Tstar, const RHOTYPE& rhostar) const{
        std::common_type_t<TTYPE, RHOTYPE> summer = 0.0;
        for (auto [i, j, Cij] : c_Cij){
            summer += Cij*pow(Tstar, i/2.0)*powi(rhostar, j);
        }
        return forceeval(get_ahs(Tstar, rhostar) + exp(-gamma*POW2(rhostar))*rhostar*Tstar*get_DeltaB2hBH(Tstar)+summer);
    }
    
public:
    // We are in "simulation units", so R is 1.0, and T and rho that go into alphar are actually T^* and rho^*
    template<typename MoleFracType>
    double R(const MoleFracType &) const { return 1.0; }
    
    template<typename TTYPE, typename RHOTYPE, typename MoleFracType>
    auto alphar(const TTYPE& Tstar, const RHOTYPE& rhostar, const MoleFracType& /*molefrac*/) const {
        return forceeval(get_a(Tstar, rhostar)/Tstar);
    }
};
 
};
 
namespace teqp::mie::lennardjones::Johnson {
 
class LJ126Johnson1993 {
    
private:
    template<typename T>
    auto POW2(const T& x) const -> T{
        return x*x;
    }
    
    template<typename T>
    auto POW3(const T& x) const -> T{
        return POW2(x)*x;
    }
    
    template<typename T>
    auto POW4(const T& x) const -> T{
        return POW2(x)*POW2(x);
    }
    
    const double gamma = 3.0;
    const std::vector<double> x {
        0.0, // placeholder for i=0 term since C++ uses 0-based indexing
        0.8623085097507421,
        2.976218765822098,
        -8.402230115796038,
        0.1054136629203555,
        -0.8564583828174598,
        1.582759470107601,
        0.7639421948305453,
        1.753173414312048,
        2.798291772190376e03,
        -4.8394220260857657e-2,
        0.9963265197721935,
        -3.698000291272493e01,
        2.084012299434647e01,
        8.305402124717285e01,
        -9.574799715203068e02,
        -1.477746229234994e02,
        
        6.398607852471505e01,
        1.603993673294834e01,
        6.805916615864377e01,
        -2.791293578795945e03,
        -6.245128304568454,
        -8.116836104958410e03,
        1.488735559561229e01,
        -1.059346754655084e04,
        -1.131607632802822e02,
        -8.867771540418822e03,
        -3.986982844450543e01,
        -4.689270299917261e03,
        2.593535277438717e02,
        -2.694523589434903e03,
        -7.218487631550215e02,
        1.721802063863269e02
    };
    
    // Table 5
    template<typename TTYPE>
    auto get_ai(const int i, const TTYPE& Tstar) const -> TTYPE{
        switch(i){
            case 1:
                return x[1]*Tstar + x[2]*sqrt(Tstar) + x[3] + x[4]/Tstar + x[5]/POW2(Tstar);
            case 2:
                return x[6]*Tstar + x[7] + x[8]/Tstar + x[9]/POW2(Tstar);
            case 3:
                return x[10]*Tstar + x[11] + x[12]/Tstar;
            case 4:
                return x[13];
            case 5:
                return x[14]/Tstar + x[15]/POW2(Tstar);
            case 6:
                return x[16]/Tstar;
            case 7:
                return x[17]/Tstar + x[18]/POW2(Tstar);
            case 8:
                return x[19]/POW2(Tstar);
            default:
                throw teqp::InvalidArgument("i is not possible in get_ai");
        }
    }
    
    // Table 6
    template<typename TTYPE>
    auto get_bi(const int i, const TTYPE& Tstar) const -> TTYPE{
        switch(i){
            case 1:
                return x[20]/POW2(Tstar) + x[21]/POW3(Tstar);
            case 2:
                return x[22]/POW2(Tstar) + x[23]/POW4(Tstar);
            case 3:
                return x[24]/POW2(Tstar) + x[25]/POW3(Tstar);
            case 4:
                return x[26]/POW2(Tstar) + x[27]/POW4(Tstar);
            case 5:
                return x[28]/POW2(Tstar) + x[29]/POW3(Tstar);
            case 6:
                return x[30]/POW2(Tstar) + x[31]/POW3(Tstar) + x[32]/POW4(Tstar);
            default:
                throw teqp::InvalidArgument("i is not possible in get_bi");
        }
    }
    
    // Table 7
    template<typename FTYPE, typename RHOTYPE>
    auto get_Gi(const int i, const FTYPE& F, const RHOTYPE& rhostar) const -> RHOTYPE{
        if (i == 1){
            return forceeval((1.0-F)/(2.0*gamma));
        }
        else{
            // Recursive definition of the other terms;
            return forceeval(-(F*powi(rhostar, 2*(i-1)) - 2.0*(i-1)*get_Gi(i-1, F, rhostar))/(2.0*gamma));
        }
    }
    
    template<typename TTYPE, typename RHOTYPE>
    auto get_alphar(const TTYPE& Tstar, const RHOTYPE& rhostar) const{
        std::common_type_t<TTYPE, RHOTYPE> summer = 0.0;
        auto F = exp(-gamma*POW2(rhostar));
        for (int i = 1; i <= 8; ++i){
            summer += get_ai(i, Tstar)*powi(rhostar, i)/static_cast<double>(i);
        }
        for (int i = 1; i <= 6; ++i){
            summer += get_bi(i, Tstar)*get_Gi(i, F, rhostar);
        }
        return forceeval(summer);
    }
    
public:
    // We are in "simulation units", so R is 1.0, and T and rho that
    // go into alphar are actually T^* and rho^*
    template<typename MoleFracType>
    double R(const MoleFracType &) const { return 1.0; }
    
    template<typename TTYPE, typename RHOTYPE, typename MoleFracType>
    auto alphar(const TTYPE& Tstar, const RHOTYPE& rhostar, const MoleFracType& /*molefrac*/) const {
        return forceeval(get_alphar(Tstar, rhostar)/Tstar);
    }
};
 
};