//================================================================================================
void LiquidTransport::set_Grad_X(const doublereal* const grad_X) {
size_t itop = m_nDim * m_nsp;
for (size_t i = 0; i < itop; i++) {
m_Grad_X[i] = grad_X[i];
}
update_Grad_lnAC();
}
void LiquidTransport::stefan_maxwell_solve()
{
doublereal tmp;
m_B.resize(m_nsp, m_nDim, 0.0);
m_A.resize(m_nsp, m_nsp, 0.0);
//! grab a local copy of the molecular weights
const vector_fp& M = m_thermo->molecularWeights();
//! grad a local copy of the ion molar volume (inverse total ion concentration)
const doublereal vol = m_thermo->molarVolume();
/*
* Update the temperature, concentrations and diffusion coefficients in the mixture.
*/
update_T();
update_C();
if (!m_diff_temp_ok) {
updateDiff_T();
}
double T = m_thermo->temperature();
update_Grad_lnAC();
m_thermo->getActivityCoefficients(DATA_PTR(m_actCoeff));
/*
* Calculate the electrochemical potential gradient. This is the
* driving force for relative diffusional transport.
*
* Here we calculate
*
* X_i * (grad (mu_i) + S_i grad T - M_i / dens * grad P
*
* This is Eqn. 13-1 p. 318 Newman. The original equation is from
* Hershfeld, Curtis, and Bird.
*
* S_i is the partial molar entropy of species i. This term will cancel
* out a lot of the grad T terms in grad (mu_i), therefore simplifying
* the expression.
*
* Ok I think there may be many ways to do this. One way is to do it via basis
* functions, at the nodes, as a function of the variables in the problem.
*
* For calculation of molality based thermo systems, we current get
* the molar based values. This may change.
*
* Note, we have broken the symmetry of the matrix here, due to
* considerations involving species concentrations going to zero.
*/
for (size_t a = 0; a < m_nDim; a++) {
for (size_t i = 0; i < m_nsp; i++) {
m_Grad_mu[a*m_nsp + i] =
m_chargeSpecies[i] * Faraday * m_Grad_V[a]
+ GasConstant * T * m_Grad_lnAC[a*m_nsp+i];
}
}
if (m_thermo->activityConvention() == cAC_CONVENTION_MOLALITY) {
int iSolvent = 0;
double mwSolvent = m_thermo->molecularWeight(iSolvent);
double mnaught = mwSolvent/ 1000.;
double lnmnaught = log(mnaught);
for (size_t a = 0; a < m_nDim; a++) {
for (size_t i = 1; i < m_nsp; i++) {
m_Grad_mu[a*m_nsp + i] -=
m_molefracs[i] * GasConstant * m_Grad_T[a] * lnmnaught;
}
}
}
/*
* Just for Note, m_A(i,j) refers to the ith row and jth column.
* They are still fortran ordered, so that i varies fastest.
*/
double condSum1;
const doublereal invRT = 1.0 / (GasConstant * T);
switch (m_nDim) {
case 1: /* 1-D approximation */
m_B(0,0) = 0.0;
//equation for the reference velocity
for (size_t j = 0; j < m_nsp; j++) {
if (m_velocityBasis == VB_MOLEAVG) {
m_A(0,j) = m_molefracs_tran[j];
} else if (m_velocityBasis == VB_MASSAVG) {
m_A(0,j) = m_massfracs_tran[j];
} else if ((m_velocityBasis >= 0)
&& (m_velocityBasis < static_cast<int>(m_nsp))) {
// use species number m_velocityBasis as reference velocity
if (m_velocityBasis == static_cast<int>(j)) {
m_A(0,j) = 1.0;
} else {
m_A(0,j) = 0.0;
}
} else {
throw CanteraError("LiquidTransport::stefan_maxwell_solve",
"Unknown reference velocity provided.");
}
}
for (size_t i = 1; i < m_nsp; i++) {
m_B(i,0) = m_Grad_mu[i] * invRT;
m_A(i,i) = 0.0;
for (size_t j = 0; j < m_nsp; j++) {
if (j != i) {
tmp = m_molefracs_tran[j] * m_bdiff(i,j);
m_A(i,i) -= tmp;
m_A(i,j) = tmp;
}
}
}
//! invert and solve the system Ax = b. Answer is in m_B
solve(m_A, m_B);
condSum1 = 0;
for (size_t i = 0; i < m_nsp; i++) {
condSum1 -= Faraday*m_chargeSpecies[i]*m_B(i,0)*m_molefracs_tran[i]/vol;
}
break;
case 2: /* 2-D approximation */
m_B(0,0) = 0.0;
m_B(0,1) = 0.0;
//equation for the reference velocity
for (size_t j = 0; j < m_nsp; j++) {
if (m_velocityBasis == VB_MOLEAVG) {
m_A(0,j) = m_molefracs_tran[j];
} else if (m_velocityBasis == VB_MASSAVG) {
m_A(0,j) = m_massfracs_tran[j];
} else if ((m_velocityBasis >= 0)
&& (m_velocityBasis < static_cast<int>(m_nsp))) {
// use species number m_velocityBasis as reference velocity
if (m_velocityBasis == static_cast<int>(j)) {
m_A(0,j) = 1.0;
} else {
m_A(0,j) = 0.0;
}
} else {
throw CanteraError("LiquidTransport::stefan_maxwell_solve",
"Unknown reference velocity provided.");
}
}
for (size_t i = 1; i < m_nsp; i++) {
m_B(i,0) = m_Grad_mu[i] * invRT;
m_B(i,1) = m_Grad_mu[m_nsp + i] * invRT;
m_A(i,i) = 0.0;
for (size_t j = 0; j < m_nsp; j++) {
if (j != i) {
tmp = m_molefracs_tran[j] * m_bdiff(i,j);
m_A(i,i) -= tmp;
m_A(i,j) = tmp;
}
}
}
//! invert and solve the system Ax = b. Answer is in m_B
solve(m_A, m_B);
break;
case 3: /* 3-D approximation */
m_B(0,0) = 0.0;
m_B(0,1) = 0.0;
m_B(0,2) = 0.0;
//equation for the reference velocity
for (size_t j = 0; j < m_nsp; j++) {
if (m_velocityBasis == VB_MOLEAVG) {
m_A(0,j) = m_molefracs_tran[j];
} else if (m_velocityBasis == VB_MASSAVG) {
m_A(0,j) = m_massfracs_tran[j];
} else if ((m_velocityBasis >= 0)
&& (m_velocityBasis < static_cast<int>(m_nsp))) {
// use species number m_velocityBasis as reference velocity
if (m_velocityBasis == static_cast<int>(j)) {
m_A(0,j) = 1.0;
} else {
m_A(0,j) = 0.0;
}
} else {
throw CanteraError("LiquidTransport::stefan_maxwell_solve",
"Unknown reference velocity provided.");
}
}
for (size_t i = 1; i < m_nsp; i++) {
m_B(i,0) = m_Grad_mu[i] * invRT;
m_B(i,1) = m_Grad_mu[m_nsp + i] * invRT;
m_B(i,2) = m_Grad_mu[2*m_nsp + i] * invRT;
m_A(i,i) = 0.0;
for (size_t j = 0; j < m_nsp; j++) {
if (j != i) {
tmp = m_molefracs_tran[j] * m_bdiff(i,j);
m_A(i,i) -= tmp;
m_A(i,j) = tmp;
}
}
}
//! invert and solve the system Ax = b. Answer is in m_B
solve(m_A, m_B);
break;
default:
printf("unimplemented\n");
throw CanteraError("routine", "not done");
break;
}
for (size_t a = 0; a < m_nDim; a++) {
for (size_t j = 0; j < m_nsp; j++) {
m_Vdiff(j,a) = m_B(j,a);
m_flux(j,a) = concTot_ * M[j] * m_molefracs_tran[j] * m_B(j,a);
}
}
}
