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density_iteration.rs
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188 lines (174 loc) · 6.86 KB
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use crate::equation_of_state::EquationOfState;
use crate::errors::{EosError, EosResult};
use crate::state::State;
use crate::EosUnit;
use quantity::si::{SIArray1, SINumber, SIUnit};
use std::sync::Arc;
pub fn density_iteration<E: EquationOfState>(
eos: &Arc<E>,
temperature: SINumber,
pressure: SINumber,
moles: &SIArray1,
initial_density: SINumber,
) -> EosResult<State<E>> {
let maxdensity = eos.max_density(Some(moles))?;
let (abstol, reltol) = (1e-12, 1e-14);
let n = moles.sum();
let mut rho = initial_density;
if rho <= 0.0 * SIUnit::reference_density() {
return Err(EosError::InvalidState(
String::from("density iteration"),
String::from("density"),
rho.to_reduced(SIUnit::reference_density())?,
));
}
let maxiter = 50;
let mut iterations = 0;
'iteration: for k in 0..maxiter {
iterations += 1;
let (mut p, mut dp_drho) = State::new_nvt(eos, temperature, n / rho, moles)?.p_dpdrho();
// attempt to correct for poor initial density rho_init
if dp_drho.is_sign_negative() && k == 0 {
rho = if initial_density <= 0.15 * maxdensity {
0.05 * initial_density
} else {
(1.1 * initial_density).min(maxdensity)?
};
let p_ = State::new_nvt(eos, temperature, n / rho, moles)?.p_dpdrho();
p = p_.0;
dp_drho = p_.1;
}
let mut error = p - pressure;
let mut delta_rho = -error / dp_drho;
if delta_rho.abs() > 0.075 * maxdensity {
delta_rho = 0.075 * maxdensity * delta_rho.signum();
};
delta_rho = delta_rho.max(-0.95 * rho)?; // prevent stepping to rho < 0.0
// correction for instable region
if dp_drho.is_sign_negative() && k < maxiter {
let d2pdrho2 = State::new_nvt(eos, temperature, n / rho, moles)?
.d2pdrho2()
.2;
if rho > 0.85 * maxdensity {
let [sp_p, sp_rho] = pressure_spinodal(eos, temperature, initial_density, moles)?;
rho = sp_rho;
error = sp_p - pressure;
if rho > 0.85 * maxdensity {
if error.is_sign_negative() {
return Err(EosError::IterationFailed(String::from("density_iteration")));
} else {
rho = rho * 0.98
}
} else if error.is_sign_positive() {
rho = 0.001 * maxdensity
} else {
rho = (rho * 1.1).min(maxdensity)?
}
} else if error.is_sign_positive() && d2pdrho2.is_sign_positive() {
let [sp_p, sp_rho] = pressure_spinodal(eos, temperature, initial_density, moles)?;
rho = sp_rho;
error = sp_p - pressure;
if error.is_sign_positive() {
rho = 0.001 * maxdensity
} else {
rho = (rho * 1.1).min(maxdensity)?
}
} else if error.is_sign_negative() && d2pdrho2.is_sign_negative() {
let [sp_p, sp_rho] = pressure_spinodal(eos, temperature, initial_density, moles)?;
rho = sp_rho;
error = sp_p - pressure;
if error.is_sign_negative() {
rho = 0.8 * maxdensity
} else {
rho = rho * 0.8
}
} else if error.is_sign_negative() && d2pdrho2.is_sign_positive() {
let [_, rho_l] = pressure_spinodal(eos, temperature, 0.8 * maxdensity, moles)?;
let [sp_v_p, rho_v] =
pressure_spinodal(eos, temperature, 0.001 * maxdensity, moles)?;
error = sp_v_p - pressure;
if error.is_sign_positive()
&& (initial_density - rho_v).abs() < (initial_density - rho_l).abs()
{
rho = 0.8 * rho_v
} else {
rho = (rho_l * 1.1).min(maxdensity)?
}
} else if error.is_sign_positive() && d2pdrho2.is_sign_negative() {
let [_, rho_l] = pressure_spinodal(eos, temperature, 0.8 * maxdensity, moles)?;
let [sp_v_p, rho_v] =
pressure_spinodal(eos, temperature, 0.001 * maxdensity, moles)?;
error = sp_v_p - pressure;
if error.is_sign_negative()
&& (initial_density - rho_v).abs() > (initial_density - rho_l).abs()
{
rho = (rho_l * 1.1).min(maxdensity)?
} else {
rho = 0.8 * rho_v
}
} else {
rho = (rho + initial_density) * 0.5;
if (rho - initial_density)
.to_reduced(SIUnit::reference_density())?
.abs()
< 1e-8
{
rho = (rho + 0.1 * maxdensity).min(maxdensity)?
}
}
continue 'iteration;
}
// Newton step
rho += delta_rho;
if error.to_reduced(SIUnit::reference_pressure())?.abs()
< f64::max(
abstol,
(rho * reltol).to_reduced(SIUnit::reference_density())?,
)
{
break 'iteration;
}
}
if iterations == maxiter + 1 {
Err(EosError::NotConverged("density_iteration".to_owned()))
} else {
Ok(State::new_nvt(eos, temperature, n / rho, moles)?)
}
}
fn pressure_spinodal<E: EquationOfState>(
eos: &Arc<E>,
temperature: SINumber,
rho_init: SINumber,
moles: &SIArray1,
) -> EosResult<[SINumber; 2]> {
let maxiter = 30;
let abstol = 1e-8;
let maxdensity = eos.max_density(Some(moles))?;
let n = moles.sum();
let mut rho = rho_init;
if rho <= 0.0 * SIUnit::reference_density() {
return Err(EosError::InvalidState(
String::from("pressure spinodal"),
String::from("density"),
rho.to_reduced(SIUnit::reference_density())?,
));
}
for _ in 0..maxiter {
let (p, dpdrho, d2pdrho2) = State::new_nvt(eos, temperature, n / rho, moles)?.d2pdrho2();
let mut delta_rho = -dpdrho / d2pdrho2;
if delta_rho.abs() > 0.05 * maxdensity {
delta_rho = 0.05 * maxdensity * delta_rho.signum()
}
delta_rho = delta_rho.max(-rho * 0.95)?; // prevent stepping to rho < 0.0
delta_rho = delta_rho.min(maxdensity - rho)?; // prevent stepping to rho > maxdensity
rho += delta_rho;
if dpdrho
.to_reduced(SIUnit::reference_pressure() / SIUnit::reference_density())?
.abs()
< abstol
{
return Ok([p, rho]);
}
}
Err(EosError::NotConverged("pressure_spinodal".to_owned()))
}