StFlow.cpp

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/**
 * @file StFlow.cpp
 */
// Copyright 2002  California Institute of Technology

#include "cantera/oneD/StFlow.h"
#include "cantera/base/ctml.h"
#include "cantera/transport/TransportBase.h"
#include "cantera/numerics/funcs.h"

#include <cstdio>

using namespace std;

namespace Cantera
{

StFlow::StFlow(IdealGasPhase* ph, size_t nsp, size_t points) :
    Domain1D(nsp+4, points),
    m_press(-1.0),
    m_nsp(nsp),
    m_thermo(0),
    m_kin(0),
    m_trans(0),
    m_jac(0),
    m_epsilon_left(0.0),
    m_epsilon_right(0.0),
    m_do_soret(false),
    m_transport_option(-1),
    m_do_radiation(false)
{
    m_type = cFlowType;

    m_points = points;
    m_thermo = ph;

    if (ph == 0) {
        return;    // used to create a dummy object
    }

    size_t nsp2 = m_thermo->nSpecies();
    if (nsp2 != m_nsp) {
        m_nsp = nsp2;
        Domain1D::resize(m_nsp+4, points);
    }


    // make a local copy of the species molecular weight vector
    m_wt = m_thermo->molecularWeights();

    // the species mass fractions are the last components in the solution
    // vector, so the total number of components is the number of species
    // plus the offset of the first mass fraction.
    m_nv = c_offset_Y + m_nsp;

    // enable all species equations by default
    m_do_species.resize(m_nsp, true);

    // but turn off the energy equation at all points
    m_do_energy.resize(m_points,false);

    m_diff.resize(m_nsp*m_points);
    m_multidiff.resize(m_nsp*m_nsp*m_points);
    m_flux.resize(m_nsp,m_points);
    m_wdot.resize(m_nsp,m_points, 0.0);
    m_ybar.resize(m_nsp);
    m_qdotRadiation.resize(m_points, 0.0);

    //-------------- default solution bounds --------------------

    setBounds(0, -1e20, 1e20); // no bounds on u
    setBounds(1, -1e20, 1e20); // V
    setBounds(2, 200.0, 1e9); // temperature bounds
    setBounds(3, -1e20, 1e20); // lambda should be negative

    // mass fraction bounds
    for (size_t k = 0; k < m_nsp; k++) {
        setBounds(4+k, -1.0e-5, 1.0e5);
    }

    //-------------------- default error tolerances ----------------
    setTransientTolerances(1.0e-8, 1.0e-15);
    setSteadyTolerances(1.0e-8, 1.0e-15);

    //-------------------- grid refinement -------------------------
    m_refiner->setActive(0, false);
    m_refiner->setActive(1, false);
    m_refiner->setActive(2, false);
    m_refiner->setActive(3, false);

    vector_fp gr;
    for (size_t ng = 0; ng < m_points; ng++) {
        gr.push_back(1.0*ng/m_points);
    }
    setupGrid(m_points, DATA_PTR(gr));
    setID("stagnation flow");

    // Find indices for radiating species
    m_kRadiating.resize(2, npos);
    size_t kr = m_thermo->speciesIndex("CO2");
    m_kRadiating[0] = (kr != npos) ? kr : m_thermo->speciesIndex("co2");
    kr = m_thermo->speciesIndex("H2O");
    m_kRadiating[1] = (kr != npos) ? kr : m_thermo->speciesIndex("h2o");
}

void StFlow::resize(size_t ncomponents, size_t points)
{
    Domain1D::resize(ncomponents, points);
    m_rho.resize(m_points, 0.0);
    m_wtm.resize(m_points, 0.0);
    m_cp.resize(m_points, 0.0);
    m_visc.resize(m_points, 0.0);
    m_tcon.resize(m_points, 0.0);

    if (m_transport_option ==  c_Mixav_Transport) {
        m_diff.resize(m_nsp*m_points);
    } else {
        m_multidiff.resize(m_nsp*m_nsp*m_points);
        m_diff.resize(m_nsp*m_points);
        m_dthermal.resize(m_nsp, m_points, 0.0);
    }
    m_flux.resize(m_nsp,m_points);
    m_wdot.resize(m_nsp,m_points, 0.0);
    m_do_energy.resize(m_points,false);
    m_qdotRadiation.resize(m_points, 0.0);

    m_fixedy.resize(m_nsp, m_points);
    m_fixedtemp.resize(m_points);

    m_dz.resize(m_points-1);
    m_z.resize(m_points);
}

void StFlow::setupGrid(size_t n, const doublereal* z)
{
    resize(m_nv, n);
    size_t j;

    m_z[0] = z[0];
    for (j = 1; j < m_points; j++) {
        if (z[j] <= z[j-1]) {
            throw CanteraError("StFlow::setupGrid",
                               "grid points must be monotonically increasing");
        }
        m_z[j] = z[j];
        m_dz[j-1] = m_z[j] - m_z[j-1];
    }
}

void StFlow::setTransport(Transport& trans, bool withSoret)
{
    m_trans = &trans;
    m_do_soret = withSoret;

    int model = m_trans->model();
    if (model == cMulticomponent || model == CK_Multicomponent) {
        m_transport_option = c_Multi_Transport;
        m_multidiff.resize(m_nsp*m_nsp*m_points);
        m_diff.resize(m_nsp*m_points);
        m_dthermal.resize(m_nsp, m_points, 0.0);
    } else if (model == cMixtureAveraged || model == CK_MixtureAveraged) {
        m_transport_option = c_Mixav_Transport;
        m_diff.resize(m_nsp*m_points);
        if (withSoret)
            throw CanteraError("setTransport",
                               "Thermal diffusion (the Soret effect) "
                               "requires using a multicomponent transport model.");
    } else {
        throw CanteraError("setTransport","unknown transport model.");
    }
}

void StFlow::enableSoret(bool withSoret)
{
    if (m_transport_option == c_Multi_Transport) {
        m_do_soret = withSoret;
    } else {
        throw CanteraError("setTransport",
                           "Thermal diffusion (the Soret effect) "
                           "requires using a multicomponent transport model.");
    }
}

void StFlow::setGas(const doublereal* x, size_t j)
{
    m_thermo->setTemperature(T(x,j));
    const doublereal* yy = x + m_nv*j + c_offset_Y;
    m_thermo->setMassFractions_NoNorm(yy);
    m_thermo->setPressure(m_press);
}

void StFlow::setGasAtMidpoint(const doublereal* x, size_t j)
{
    m_thermo->setTemperature(0.5*(T(x,j)+T(x,j+1)));
    const doublereal* yyj = x + m_nv*j + c_offset_Y;
    const doublereal* yyjp = x + m_nv*(j+1) + c_offset_Y;
    for (size_t k = 0; k < m_nsp; k++) {
        m_ybar[k] = 0.5*(yyj[k] + yyjp[k]);
    }
    m_thermo->setMassFractions_NoNorm(DATA_PTR(m_ybar));
    m_thermo->setPressure(m_press);
}

void StFlow::_finalize(const doublereal* x)
{
    size_t k, j;
    doublereal zz, tt;
    size_t nz = m_zfix.size();
    bool e = m_do_energy[0];
    for (j = 0; j < m_points; j++) {
        if (e || nz == 0) {
            m_fixedtemp[j] = T(x, j);
        } else {
            zz = (z(j) - z(0))/(z(m_points - 1) - z(0));
            tt = linearInterp(zz, m_zfix, m_tfix);
            m_fixedtemp[j] = tt;
        }
        for (k = 0; k < m_nsp; k++) {
            setMassFraction(j, k, Y(x, k, j));
        }
    }
    if (e) {
        solveEnergyEqn();
    }
}

void StFlow::eval(size_t jg, doublereal* xg,
                  doublereal* rg, integer* diagg, doublereal rdt)
{
    // if evaluating a Jacobian, and the global point is outside
    // the domain of influence for this domain, then skip
    // evaluating the residual
    if (jg != npos && (jg + 1 < firstPoint() || jg > lastPoint() + 1)) {
        return;
    }

    // if evaluating a Jacobian, compute the steady-state residual
    if (jg != npos) {
        rdt = 0.0;
    }

    // start of local part of global arrays
    doublereal* x = xg + loc();
    doublereal* rsd = rg + loc();
    integer* diag = diagg + loc();

    size_t jmin, jmax;

    if (jg == npos) {      // evaluate all points
        jmin = 0;
        jmax = m_points - 1;
    } else {          // evaluate points for Jacobian
        size_t jpt = (jg == 0) ? 0 : jg - firstPoint();
        jmin = std::max<size_t>(jpt, 1) - 1;
        jmax = std::min(jpt+1,m_points-1);
    }

    // properties are computed for grid points from j0 to j1
    size_t j0 = std::max<size_t>(jmin, 1) - 1;
    size_t j1 = std::min(jmax+1,m_points-1);

    size_t j, k;

    //-----------------------------------------------------
    //              update properties
    //-----------------------------------------------------

    updateThermo(x, j0, j1);
    // update transport properties only if a Jacobian is not being evaluated
    if (jg == npos) {
        updateTransport(x, j0, j1);
    }

    // update the species diffusive mass fluxes whether or not a
    // Jacobian is being evaluated
    updateDiffFluxes(x, j0, j1);


    //----------------------------------------------------
    // evaluate the residual equations at all required
    // grid points
    //----------------------------------------------------

    doublereal sum, sum2, dtdzj;

    // calculation of qdotRadiation

    // The simple radiation model used was established by Y. Liu and B. Rogg [Y.
    // Liu and B. Rogg, Modelling of thermally radiating diffusion flames with
    // detailed chemistry and transport, EUROTHERM Seminars, 17:114-127, 1991].
    // This model uses the optically thin limit and the gray-gas approximation
    // to simply calculate a volume specified heat flux out of the Planck
    // absorption coefficients, the boundary emissivities and the temperature.
    // The model considers only CO2 and H2O as radiating species. Polynomial
    // lines calculate the species Planck coefficients for H2O and CO2. The data
    // for the lines is taken from the RADCAL program [Grosshandler, W. L.,
    // RADCAL: A Narrow-Band Model for Radiation Calculations in a Combustion
    // Environment, NIST technical note 1402, 1993]. The coefficients for the
    // polynomials are taken from [http://www.sandia.gov/TNF/radiation.html].

    if (m_do_radiation) {
        // variable definitions for the Planck absorption coefficient and the
        // radiation calculation:
        doublereal k_P_ref = 1.0*OneAtm;

        // polynomial coefficients:
        const doublereal c_H2O[6] = {-0.23093, -1.12390, 9.41530, -2.99880,
                                     0.51382, -1.86840e-5};
        const doublereal c_CO2[6] = {18.741, -121.310, 273.500, -194.050,
                                     56.310, -5.8169};

        // calculation of the two boundary values
        double boundary_Rad_left = m_epsilon_left * StefanBoltz * pow(T(x, 0), 4);
        double boundary_Rad_right = m_epsilon_right * StefanBoltz * pow(T(x, m_points - 1), 4);

        // loop over all grid points
        for (size_t j = jmin; j < jmax; j++) {
            // helping variable for the calculation
            double radiative_heat_loss = 0;

            // calculation of the mean Planck absorption coefficient
            double k_P = 0;
            // absorption coefficient for H2O
            if (m_kRadiating[1] != npos) {
                double k_P_H2O = 0;
                for (size_t n = 0; n <= 5; n++) {
                    k_P_H2O += c_H2O[n] * pow(1000 / T(x, j), (double) n);
                }
                k_P_H2O /= k_P_ref;
                k_P += m_press * X(x, m_kRadiating[1], j) * k_P_H2O;
            }
            // absorption coefficient for CO2
            if (m_kRadiating[0] != npos) {
                double k_P_CO2 = 0;
                for (size_t n = 0; n <= 5; n++) {
                    k_P_CO2 += c_CO2[n] * pow(1000 / T(x, j), (double) n);
                }
                k_P_CO2 /= k_P_ref;
                k_P += m_press * X(x, m_kRadiating[0], j) * k_P_CO2;
            }

            // calculation of the radiative heat loss term
            radiative_heat_loss = 2 * k_P *(2 * StefanBoltz * pow(T(x, j), 4)
            - boundary_Rad_left - boundary_Rad_right);

            // set the radiative heat loss vector
            m_qdotRadiation[j] = radiative_heat_loss;
        }
    }

    for (j = jmin; j <= jmax; j++) {
        //----------------------------------------------
        //         left boundary
        //----------------------------------------------

        if (j == 0) {

            // these may be modified by a boundary object

            // Continuity. This propagates information right-to-left,
            // since rho_u at point 0 is dependent on rho_u at point 1,
            // but not on mdot from the inlet.
            rsd[index(c_offset_U,0)] =
                -(rho_u(x,1) - rho_u(x,0))/m_dz[0]
                -(density(1)*V(x,1) + density(0)*V(x,0));

            // the inlet (or other) object connected to this one
            // will modify these equations by subtracting its values
            // for V, T, and mdot. As a result, these residual equations
            // will force the solution variables to the values for
            // the boundary object
            rsd[index(c_offset_V,0)] = V(x,0);
            rsd[index(c_offset_T,0)] = T(x,0);
            rsd[index(c_offset_L,0)] = -rho_u(x,0);

            // The default boundary condition for species is zero
            // flux. However, the boundary object may modify
            // this.
            sum = 0.0;
            for (k = 0; k < m_nsp; k++) {
                sum += Y(x,k,0);
                rsd[index(c_offset_Y + k, 0)] =
                    -(m_flux(k,0) + rho_u(x,0)* Y(x,k,0));
            }
            rsd[index(c_offset_Y, 0)] = 1.0 - sum;
        }

        else if (j == m_points - 1) {
            evalRightBoundary(x, rsd, diag, rdt);

        } else { // interior points
            evalContinuity(j, x, rsd, diag, rdt);

            //------------------------------------------------
            //    Radial momentum equation
            //
            //    \rho dV/dt + \rho u dV/dz + \rho V^2
            //       = d(\mu dV/dz)/dz - lambda
            //
            //-------------------------------------------------
            rsd[index(c_offset_V,j)]
            = (shear(x,j) - lambda(x,j) - rho_u(x,j)*dVdz(x,j)
               - m_rho[j]*V(x,j)*V(x,j))/m_rho[j]
              - rdt*(V(x,j) - V_prev(j));
            diag[index(c_offset_V, j)] = 1;

            //-------------------------------------------------
            //    Species equations
            //
            //   \rho dY_k/dt + \rho u dY_k/dz + dJ_k/dz
            //   = M_k\omega_k
            //
            //-------------------------------------------------
            getWdot(x,j);

            doublereal convec, diffus;
            for (k = 0; k < m_nsp; k++) {
                convec = rho_u(x,j)*dYdz(x,k,j);
                diffus = 2.0*(m_flux(k,j) - m_flux(k,j-1))
                         /(z(j+1) - z(j-1));
                rsd[index(c_offset_Y + k, j)]
                = (m_wt[k]*(wdot(k,j))
                   - convec - diffus)/m_rho[j]
                  - rdt*(Y(x,k,j) - Y_prev(k,j));
                diag[index(c_offset_Y + k, j)] = 1;
            }

            //-----------------------------------------------
            //    energy equation
            //
            //    \rho c_p dT/dt + \rho c_p u dT/dz
            //    = d(k dT/dz)/dz
            //      - sum_k(\omega_k h_k_ref)
            //      - sum_k(J_k c_p_k / M_k) dT/dz
            //-----------------------------------------------

            if (m_do_energy[j]) {

                setGas(x,j);

                // heat release term
                const vector_fp& h_RT = m_thermo->enthalpy_RT_ref();
                const vector_fp& cp_R = m_thermo->cp_R_ref();

                sum = 0.0;
                sum2 = 0.0;
                doublereal flxk;
                for (k = 0; k < m_nsp; k++) {
                    flxk = 0.5*(m_flux(k,j-1) + m_flux(k,j));
                    sum += wdot(k,j)*h_RT[k];
                    sum2 += flxk*cp_R[k]/m_wt[k];
                }
                sum *= GasConstant * T(x,j);
                dtdzj = dTdz(x,j);
                sum2 *= GasConstant * dtdzj;

                rsd[index(c_offset_T, j)]   =
                    - m_cp[j]*rho_u(x,j)*dtdzj
                    - divHeatFlux(x,j) - sum - sum2;
                rsd[index(c_offset_T, j)] /= (m_rho[j]*m_cp[j]);

                rsd[index(c_offset_T, j)] -= rdt*(T(x,j) - T_prev(j));
                rsd[index(c_offset_T, j)] -= (m_qdotRadiation[j] / (m_rho[j] * m_cp[j]));
                diag[index(c_offset_T, j)] = 1;
            } else {
                // residual equations if the energy equation is disabled
                rsd[index(c_offset_T, j)] = T(x,j) - T_fixed(j);
                diag[index(c_offset_T, j)] = 0;
            }

            rsd[index(c_offset_L, j)] = lambda(x,j) - lambda(x,j-1);
            diag[index(c_offset_L, j)] = 0;
        }
    }
}

void StFlow::updateTransport(doublereal* x, size_t j0, size_t j1)
{
    if (m_transport_option == c_Mixav_Transport) {
        for (size_t j = j0; j < j1; j++) {
            setGasAtMidpoint(x,j);
            m_visc[j] = (m_dovisc ? m_trans->viscosity() : 0.0);
            m_trans->getMixDiffCoeffs(DATA_PTR(m_diff) + j*m_nsp);
            m_tcon[j] = m_trans->thermalConductivity();
        }
    } else if (m_transport_option == c_Multi_Transport) {
        for (size_t j = j0; j < j1; j++) {
            setGasAtMidpoint(x,j);
            doublereal wtm = m_thermo->meanMolecularWeight();
            doublereal rho = m_thermo->density();
            m_visc[j] = (m_dovisc ? m_trans->viscosity() : 0.0);
            m_trans->getMultiDiffCoeffs(m_nsp, &m_multidiff[mindex(0,0,j)]);

            // Use m_diff as storage for the factor outside the summation
            for (size_t k = 0; k < m_nsp; k++) {
                m_diff[k+j*m_nsp] = m_wt[k] * rho / (wtm*wtm);
            }

            m_tcon[j] = m_trans->thermalConductivity();
            if (m_do_soret) {
                m_trans->getThermalDiffCoeffs(m_dthermal.ptrColumn(0) + j*m_nsp);
            }
        }
    }
}

void StFlow::showSolution(const doublereal* x)
{
    size_t nn = m_nv/5;
    size_t i, j, n;
    char buf[100];

    // The mean molecular weight is needed to convert
    updateThermo(x, 0, m_points-1);

    sprintf(buf, "    Pressure:  %10.4g Pa \n", m_press);
    writelog(buf);
    for (i = 0; i < nn; i++) {
        writeline('-', 79, false, true);
        sprintf(buf, "\n        z   ");
        writelog(buf);
        for (n = 0; n < 5; n++) {
            sprintf(buf, " %10s ",componentName(i*5 + n).c_str());
            writelog(buf);
        }
        writeline('-', 79, false, true);
        for (j = 0; j < m_points; j++) {
            sprintf(buf, "\n %10.4g ",m_z[j]);
            writelog(buf);
            for (n = 0; n < 5; n++) {
                sprintf(buf, " %10.4g ",component(x, i*5+n,j));
                writelog(buf);
            }
        }
        writelog("\n");
    }
    size_t nrem = m_nv - 5*nn;
    writeline('-', 79, false, true);
    sprintf(buf, "\n        z   ");
    writelog(buf);
    for (n = 0; n < nrem; n++) {
        sprintf(buf, " %10s ", componentName(nn*5 + n).c_str());
        writelog(buf);
    }
    writeline('-', 79, false, true);
    for (j = 0; j < m_points; j++) {
        sprintf(buf, "\n %10.4g ",m_z[j]);
        writelog(buf);
        for (n = 0; n < nrem; n++) {
            sprintf(buf, " %10.4g ",component(x, nn*5+n,j));
            writelog(buf);
        }
    }
    writelog("\n");
    if (m_do_radiation) {
        writeline('-', 79, false, true);
        sprintf(buf, "\n        z        radiative heat loss");
        writelog(buf);
        writeline('-', 79, false, true);
        for (j = 0; j < m_points; j++) {
            sprintf(buf, "\n %10.4g        %10.4g", m_z[j], m_qdotRadiation[j]);
            writelog(buf);
        }
        writelog("\n");
    }
}

void StFlow::updateDiffFluxes(const doublereal* x, size_t j0, size_t j1)
{
    size_t j, k, m;
    doublereal sum, wtm, rho, dz, gradlogT;

    switch (m_transport_option) {

    case c_Mixav_Transport:
        for (j = j0; j < j1; j++) {
            sum = 0.0;
            wtm = m_wtm[j];
            rho = density(j);
            dz = z(j+1) - z(j);

            for (k = 0; k < m_nsp; k++) {
                m_flux(k,j) = m_wt[k]*(rho*m_diff[k+m_nsp*j]/wtm);
                m_flux(k,j) *= (X(x,k,j) - X(x,k,j+1))/dz;
                sum -= m_flux(k,j);
            }
            // correction flux to insure that \sum_k Y_k V_k = 0.
            for (k = 0; k < m_nsp; k++) {
                m_flux(k,j) += sum*Y(x,k,j);
            }
        }
        break;

    case c_Multi_Transport:
        for (j = j0; j < j1; j++) {
            dz = z(j+1) - z(j);

            for (k = 0; k < m_nsp; k++) {
                doublereal sum = 0.0;
                for (size_t m = 0; m < m_nsp; m++) {
                    sum += m_wt[m] * m_multidiff[mindex(k,m,j)] * (X(x,m,j+1)-X(x,m,j));
                }
                m_flux(k,j) = sum * m_diff[k+j*m_nsp] / dz;
            }
        }
        break;

    default:
        throw CanteraError("updateDiffFluxes","unknown transport model");
    }

    if (m_do_soret) {
        for (m = j0; m < j1; m++) {
            gradlogT = 2.0 * (T(x,m+1) - T(x,m)) /
                       ((T(x,m+1) + T(x,m)) * (z(m+1) - z(m)));
            for (k = 0; k < m_nsp; k++) {
                m_flux(k,m) -= m_dthermal(k,m)*gradlogT;
            }
        }
    }
}

string StFlow::componentName(size_t n) const
{
    switch (n) {
    case 0:
        return "u";
    case 1:
        return "V";
    case 2:
        return "T";
    case 3:
        return "lambda";
    default:
        if (n >= c_offset_Y && n < (c_offset_Y + m_nsp)) {
            return m_thermo->speciesName(n - c_offset_Y);
        } else {
            return "<unknown>";
        }
    }
}

size_t StFlow::componentIndex(const std::string& name) const
{
    if (name=="u") {
        return 0;
    } else if (name=="V") {
        return 1;
    } else if (name=="T") {
        return 2;
    } else if (name=="lambda") {
        return 3;
    } else {
        for (size_t n=4; n<m_nsp+4; n++) {
            if (componentName(n)==name) {
                return n;
            }
        }
    }

    return npos;
}

void StFlow::restore(const XML_Node& dom, doublereal* soln, int loglevel)
{
    Domain1D::restore(dom, soln, loglevel);
    vector<string> ignored;
    size_t nsp = m_thermo->nSpecies();
    vector_int did_species(nsp, 0);

    vector<XML_Node*> str = dom.getChildren("string");
    for (size_t istr = 0; istr < str.size(); istr++) {
        const XML_Node& nd = *str[istr];
        writelog(nd["title"]+": "+nd.value()+"\n");
    }

    double pp = -1.0;
    pp = getFloat(dom, "pressure", "pressure");
    setPressure(pp);

    vector<XML_Node*> d = dom.child("grid_data").getChildren("floatArray");
    size_t nd = d.size();

    vector_fp x;
    size_t n, np = 0, j, ks, k;
    string nm;
    bool readgrid = false, wrote_header = false;
    for (n = 0; n < nd; n++) {
        const XML_Node& fa = *d[n];
        nm = fa["title"];
        if (nm == "z") {
            getFloatArray(fa,x,false);
            np = x.size();
            writelog("Grid contains "+int2str(np)+" points.\n", loglevel >= 2);
            readgrid = true;
            setupGrid(np, DATA_PTR(x));
        }
    }
    if (!readgrid) {
        throw CanteraError("StFlow::restore",
                           "domain contains no grid points.");
    }

    writelog("Importing datasets:\n", loglevel >= 2);
    for (n = 0; n < nd; n++) {
        const XML_Node& fa = *d[n];
        nm = fa["title"];
        getFloatArray(fa,x,false);
        if (nm == "u") {
            writelog("axial velocity   ", loglevel >= 2);
            if (x.size() != np) {
                throw CanteraError("StFlow::restore",
                                   "axial velocity array size error");
            }
            for (j = 0; j < np; j++) {
                soln[index(0,j)] = x[j];
            }
        } else if (nm == "z") {
            ;   // already read grid
        } else if (nm == "V") {
            writelog("radial velocity   ", loglevel >= 2);
            if (x.size() != np) {
                throw CanteraError("StFlow::restore",
                                   "radial velocity array size error");
            }
            for (j = 0; j < np; j++) {
                soln[index(1,j)] = x[j];
            }
        } else if (nm == "T") {
            writelog("temperature   ", loglevel >= 2);
            if (x.size() != np) {
                throw CanteraError("StFlow::restore",
                                   "temperature array size error");
            }
            for (j = 0; j < np; j++) {
                soln[index(2,j)] = x[j];
            }

            // For fixed-temperature simulations, use the
            // imported temperature profile by default.  If
            // this is not desired, call setFixedTempProfile
            // *after* restoring the solution.

            vector_fp zz(np);
            for (size_t jj = 0; jj < np; jj++) {
                zz[jj] = (grid(jj) - zmin())/(zmax() - zmin());
            }
            setFixedTempProfile(zz, x);
        } else if (nm == "L") {
            writelog("lambda   ", loglevel >= 2);
            if (x.size() != np) {
                throw CanteraError("StFlow::restore",
                                   "lambda arary size error");
            }
            for (j = 0; j < np; j++) {
                soln[index(3,j)] = x[j];
            }
        } else if (m_thermo->speciesIndex(nm) != npos) {
            writelog(nm+"   ", loglevel >= 2);
            if (x.size() == np) {
                k = m_thermo->speciesIndex(nm);
                did_species[k] = 1;
                for (j = 0; j < np; j++) {
                    soln[index(k+4,j)] = x[j];
                }
            }
        } else {
            ignored.push_back(nm);
        }
    }

    if (loglevel >=2 && !ignored.empty()) {
        writelog("\n\n");
        writelog("Ignoring datasets:\n");
        size_t nn = ignored.size();
        for (size_t n = 0; n < nn; n++) {
            writelog(ignored[n]+"   ");
        }
    }

    if (loglevel >= 1) {
        for (ks = 0; ks < nsp; ks++) {
            if (did_species[ks] == 0) {
                if (!wrote_header) {
                    writelog("Missing data for species:\n");
                    wrote_header = true;
                }
                writelog(m_thermo->speciesName(ks)+" ");
            }
        }
    }

    if (dom.hasChild("energy_enabled")) {
        getFloatArray(dom, x, false, "", "energy_enabled");
        if (x.size() == nPoints()) {
            for (size_t i = 0; i < x.size(); i++) {
                m_do_energy[i] = x[i];
            }
        } else if (!x.empty()) {
            throw CanteraError("StFlow::restore", "energy_enabled is length" +
                               int2str(x.size()) + "but should be length" +
                               int2str(nPoints()));
        }
    }

    if (dom.hasChild("species_enabled")) {
        getFloatArray(dom, x, false, "", "species_enabled");
        if (x.size() == m_nsp) {
            for (size_t i = 0; i < x.size(); i++) {
                m_do_species[i] = x[i];
            }
        } else if (!x.empty()) {
            // This may occur when restoring from a mechanism with a different
            // number of species.
            if (loglevel > 0) {
                writelog("\nWarning: StFlow::restore: species_enabled is length " +
                         int2str(x.size()) + " but should be length " +
                         int2str(m_nsp) + ". Enabling all species equations by default.");
            }
            m_do_species.assign(m_nsp, true);
        }
    }

    if (dom.hasChild("refine_criteria")) {
        XML_Node& ref = dom.child("refine_criteria");
        refiner().setCriteria(getFloat(ref, "ratio"), getFloat(ref, "slope"),
                              getFloat(ref, "curve"), getFloat(ref, "prune"));
        refiner().setGridMin(getFloat(ref, "grid_min"));
    }
}

XML_Node& StFlow::save(XML_Node& o, const doublereal* const sol)
{
    size_t k;

    Array2D soln(m_nv, m_points, sol + loc());

    XML_Node& flow = Domain1D::save(o, sol);
    flow.addAttribute("type",flowType());

    if (m_desc != "") {
        addString(flow,"description",m_desc);
    }
    XML_Node& gv = flow.addChild("grid_data");
    addFloat(flow, "pressure", m_press, "Pa", "pressure");

    addFloatArray(gv,"z",m_z.size(),DATA_PTR(m_z),
                  "m","length");
    vector_fp x(soln.nColumns());

    soln.getRow(0,DATA_PTR(x));
    addFloatArray(gv,"u",x.size(),DATA_PTR(x),"m/s","velocity");

    soln.getRow(1,DATA_PTR(x));
    addFloatArray(gv,"V",
                  x.size(),DATA_PTR(x),"1/s","rate");

    soln.getRow(2,DATA_PTR(x));
    addFloatArray(gv,"T",x.size(),DATA_PTR(x),"K","temperature");

    soln.getRow(3,DATA_PTR(x));
    addFloatArray(gv,"L",x.size(),DATA_PTR(x),"N/m^4");

    for (k = 0; k < m_nsp; k++) {
        soln.getRow(4+k,DATA_PTR(x));
        addFloatArray(gv,m_thermo->speciesName(k),
                      x.size(),DATA_PTR(x),"","massFraction");
    }
    if (m_do_radiation) {
        addFloatArray(gv, "radiative_heat_loss", m_z.size(),
            DATA_PTR(m_qdotRadiation), "W/m^3", "specificPower");
    }
    vector_fp values(nPoints());
    for (size_t i = 0; i < nPoints(); i++) {
        values[i] = m_do_energy[i];
    }
    addNamedFloatArray(flow, "energy_enabled", nPoints(), &values[0]);

    values.resize(m_nsp);
    for (size_t i = 0; i < m_nsp; i++) {
        values[i] = m_do_species[i];
    }
    addNamedFloatArray(flow, "species_enabled", m_nsp, &values[0]);

    XML_Node& ref = flow.addChild("refine_criteria");
    addFloat(ref, "ratio", refiner().maxRatio());
    addFloat(ref, "slope", refiner().maxDelta());
    addFloat(ref, "curve", refiner().maxSlope());
    addFloat(ref, "prune", refiner().prune());
    addFloat(ref, "grid_min", refiner().gridMin());

    return flow;
}

void StFlow::setJac(MultiJac* jac)
{
    m_jac = jac;
}

void AxiStagnFlow::evalRightBoundary(doublereal* x, doublereal* rsd,
                                     integer* diag, doublereal rdt)
{
    size_t j = m_points - 1;
    // the boundary object connected to the right of this one may modify or
    // replace these equations. The default boundary conditions are zero u, V,
    // and T, and zero diffusive flux for all species.

    rsd[index(0,j)] = rho_u(x,j);
    rsd[index(1,j)] = V(x,j);
    rsd[index(2,j)] = T(x,j);
    rsd[index(c_offset_L, j)] = lambda(x,j) - lambda(x,j-1);
    diag[index(c_offset_L, j)] = 0;
    doublereal sum = 0.0;
    for (size_t k = 0; k < m_nsp; k++) {
        sum += Y(x,k,j);
        rsd[index(k+4,j)] = m_flux(k,j-1) + rho_u(x,j)*Y(x,k,j);
    }
    rsd[index(4,j)] = 1.0 - sum;
    diag[index(4,j)] = 0;
}

void AxiStagnFlow::evalContinuity(size_t j, doublereal* x, doublereal* rsd,
                                  integer* diag, doublereal rdt)
{
    //----------------------------------------------
    //    Continuity equation
    //
    //    Note that this propagates the mass flow rate information to the left
    //    (j+1 -> j) from the value specified at the right boundary. The
    //    lambda information propagates in the opposite direction.
    //
    //    d(\rho u)/dz + 2\rho V = 0
    //
    //------------------------------------------------

    rsd[index(c_offset_U,j)] =
        -(rho_u(x,j+1) - rho_u(x,j))/m_dz[j]
        -(density(j+1)*V(x,j+1) + density(j)*V(x,j));

    //algebraic constraint
    diag[index(c_offset_U, j)] = 0;
}

FreeFlame::FreeFlame(IdealGasPhase* ph, size_t nsp, size_t points) :
    StFlow(ph, nsp, points),
    m_zfixed(Undef),
    m_tfixed(Undef)
{
    m_dovisc = false;
    setID("flame");
}

void FreeFlame::evalRightBoundary(doublereal* x, doublereal* rsd,
                                  integer* diag, doublereal rdt)
{
    size_t j = m_points - 1;

    // the boundary object connected to the right of this one may modify or
    // replace these equations. The default boundary conditions are zero u, V,
    // and T, and zero diffusive flux for all species.

    // zero gradient
    rsd[index(0,j)] = rho_u(x,j) - rho_u(x,j-1);
    rsd[index(1,j)] = V(x,j);
    rsd[index(2,j)] = T(x,j) - T(x,j-1);
    doublereal sum = 0.0;
    rsd[index(c_offset_L, j)] = lambda(x,j) - lambda(x,j-1);
    diag[index(c_offset_L, j)] = 0;
    for (size_t k = 0; k < m_nsp; k++) {
        sum += Y(x,k,j);
        rsd[index(k+4,j)] = m_flux(k,j-1) + rho_u(x,j)*Y(x,k,j);
    }
    rsd[index(4,j)] = 1.0 - sum;
    diag[index(4,j)] = 0;
}

void FreeFlame::evalContinuity(size_t j, doublereal* x, doublereal* rsd,
                               integer* diag, doublereal rdt)
{
    //----------------------------------------------
    //    Continuity equation
    //
    //    d(\rho u)/dz + 2\rho V = 0
    //
    //----------------------------------------------

    if (grid(j) > m_zfixed) {
        rsd[index(c_offset_U,j)] =
            - (rho_u(x,j) - rho_u(x,j-1))/m_dz[j-1]
            - (density(j-1)*V(x,j-1) + density(j)*V(x,j));
    }

    else if (grid(j) == m_zfixed) {
        if (m_do_energy[j]) {
            rsd[index(c_offset_U,j)] = (T(x,j) - m_tfixed);
        } else {
            rsd[index(c_offset_U,j)] = (rho_u(x,j)
                                        - m_rho[0]*0.3);
        }
    } else if (grid(j) < m_zfixed) {
        rsd[index(c_offset_U,j)] =
            - (rho_u(x,j+1) - rho_u(x,j))/m_dz[j]
            - (density(j+1)*V(x,j+1) + density(j)*V(x,j));
    }
    //algebraic constraint
    diag[index(c_offset_U, j)] = 0;
}

void FreeFlame::_finalize(const doublereal* x)
{
    StFlow::_finalize(x);
    // If the domain contains the temperature fixed point, make sure that it
    // is correctly set. This may be necessary when the grid has been modified
    // externally.
    if (m_tfixed != Undef) {
        for (size_t j = 0; j < m_points; j++) {
            if (z(j) == m_zfixed) {
                return; // fixed point is already set correctly
            }
        }

        for (size_t j = 0; j < m_points - 1; j++) {
            // Find where the temperature profile crosses the current
            // fixed temperature.
            if ((T(x, j) - m_tfixed) * (T(x, j+1) - m_tfixed) <= 0.0) {
                m_tfixed = T(x, j+1);
                m_zfixed = z(j+1);
                return;
            }
        }
    }
}

void FreeFlame::restore(const XML_Node& dom, doublereal* soln, int loglevel)
{
    StFlow::restore(dom, soln, loglevel);
    getOptionalFloat(dom, "t_fixed", m_tfixed);
    getOptionalFloat(dom, "z_fixed", m_zfixed);
}

XML_Node& FreeFlame::save(XML_Node& o, const doublereal* const sol)
{
    XML_Node& flow = StFlow::save(o, sol);
    if (m_zfixed != Undef) {
        addFloat(flow, "z_fixed", m_zfixed, "m");
        addFloat(flow, "t_fixed", m_tfixed, "K");
    }
    return flow;
}

}  // namespace