/// <summary>
/// Evaluate the reference state at the given point.
/// </summary>
virtual void EvaluateReferenceState(
const PhysicalConstants & phys,
double dZ,
double dLon,
double dLat,
double * dState
) const {
// 3D temperature
double dT = m_dT0 - m_dGamma * dZ;
// 3D pressure
double dPressure = phys.GetP0()
* pow(1.0 - m_dGamma / m_dT0 * dZ,
phys.GetG() / (phys.GetR() * m_dGamma));
// 3D density
double dRho = dPressure / (phys.GetR() * dT);
// Store the state
dState[0] = 0.0;
dState[1] = 0.0;
dState[2] = phys.RhoThetaFromPressure(dPressure) / dRho;
dState[3] = 0.0;
dState[4] = dRho;
}
/// <summary>
/// Evaluate the state vector at the given point.
/// </summary>
virtual void EvaluatePointwiseState(
const PhysicalConstants & phys,
const Time & time,
double dZp,
double dXp,
double dYp,
double * dState,
double * dTracer
) const {
const double dG = phys.GetG();
const double dCv = phys.GetCv();
const double dCp = phys.GetCp();
const double dRd = phys.GetR();
const double dP0 = phys.GetP0();
// The Brunt-Vaisala frequency
const double dNbar = dG / sqrt(dCp * m_dT0);
// Base potential temperature field
const double dTheta0 = m_dT0;
double dThetaBar = dTheta0 * exp(dNbar * dNbar / dG * dZp);
// Set the uniform U, V, W field for all time
dState[0] = m_dU0;
dState[1] = 0.0;
dState[3] = 0.0;
// Set the initial potential temperature field
dState[2] = dThetaBar;
// Set the initial density based on the Exner pressure
double dExnerP = exp(-dG / (dCp * m_dT0) * dZp);
double dRho = dP0 / (dRd * dThetaBar) * pow(dExnerP,(dCv / dRd));
dState[4] = dRho;
}
/// <summary>
/// Calculate eta at the given point via Newton iteration. The
/// geopotential and temperature at this point are also returned via
/// command-line parameters.
/// </summary>
double EtaFromRLL(
const PhysicalConstants &phys,
double dZp,
double dXp,
double dYp,
double & dGeopotential,
double & dTemperature
) const {
const int MaxIterations = 50;
const double InitialEta = 1.0e-5;
const double Convergence = 1.0e-13;
// Buffer variables
double dEta = InitialEta;
double dNewEta;
double dF;
double dDiffF;
// Iterate until convergence is achieved
int i = 0;
for (; i < MaxIterations; i++) {
CalculateGeopotentialTemperature(
phys, dEta, dXp, dYp, dGeopotential, dTemperature);
dF = - phys.GetG() * dZp + dGeopotential;
dDiffF = - phys.GetR() / dEta * dTemperature;
dNewEta = dEta - dF / dDiffF;
if (fabs(dEta - dNewEta) < Convergence) {
return dNewEta;
}
dEta = dNewEta;
}
// Check for convergence failure
if (i == MaxIterations) {
_EXCEPTIONT("Maximum number of iterations exceeded.");
}
if ((dEta > 1.0) || (dEta < 0.0)) {
_EXCEPTIONT("Invalid Eta value");
}
return dEta;
}
/// <summary>
/// Evaluate the reference state at the given point.
/// </summary>
virtual void EvaluateReferenceState(
const PhysicalConstants & phys,
double dZp,
double dXp,
double dYp,
double * dState
) const {
const double dG = phys.GetG();
const double dCv = phys.GetCv();
const double dCp = phys.GetCp();
const double dRd = phys.GetR();
const double dP0 = phys.GetP0();
// Base potential temperature field
double dThetaBar = m_dTheta0 * exp(m_dNbar * m_dNbar / dG * dZp);
// Set the uniform U, V, W field for all time
dState[0] = m_dU0;
dState[1] = 0.0;
dState[3] = 0.0;
// Zero gravity case
if (dG == 0.0) {
static double dT0 = 300.0;
dState[2] = dT0 * pow(dP0, (dRd / dCp));
dState[4] = dP0 / (dRd * dT0);
// Stratification with gravity
} else {
// Set the initial density based on the Exner pressure
double dExnerP = (dG * dG) / (dCp * m_dTheta0 * m_dNbar * m_dNbar);
dExnerP *= (exp(-m_dNbar * m_dNbar / dG * dZp) - 1.0);
dExnerP += 1.0;
double dRho = dP0 / (dRd * dThetaBar) * pow(dExnerP,(dCv / dRd));
dState[4] = dRho;
// Set the initial potential temperature field
//dState[2] = phys.PressureFromRhoTheta(dThetaBar * dRho);
//dState[2] = (dThetaBar * dRho);
dState[2] = dThetaBar;
}
}
/// <summary>
/// Calculate the geopotential and temperature at the given point.
/// </summary>
void CalculateGeopotentialTemperature(
const PhysicalConstants & phys,
double dEta,
double dXp,
double dYp,
double & dGeopotential,
double & dTemperature
) const {
// Get some constants
const double dG = phys.GetG();
const double dCv = phys.GetCv();
const double dCp = phys.GetCp();
const double dRd = phys.GetR();
const double dP0 = phys.GetP0();
const double dae = phys.GetEarthRadius();
const double df0 = 2 * phys.GetOmega() * sin(m_dRefLat);
//const double df0 = 0.0;
const double dbeta0 = 2 * phys.GetOmega() * cos(m_dRefLat) / dae;
//const double dbeta0 = 0.0;
const double dLy = m_dGDim[3] - m_dGDim[2];
// Horizontally averaged temperature
double dAvgTemperature =
m_dT0 * pow(dEta, dRd * m_ddTdz / dG);
// Horizontally averaged geopotential
double dAvgGeopotential =
m_dT0 * dG / m_ddTdz *
(1.0 - pow(dEta, dRd * m_ddTdz / dG));
// Horizontal variation geopotential function
double dXYGeopotential = 0.5 * m_dU0 *
((df0 - dbeta0 * m_dY0) * (dYp - m_dY0 -
m_dY0 / m_dpiC * sin(2 * m_dpiC * dYp / dLy)) +
0.5 * dbeta0 *
(dYp * dYp - dLy * dYp / m_dpiC * sin(2 * m_dpiC * dYp / dLy) -
0.5 * dLy * dLy / (m_dpiC * m_dpiC) * cos(2 * m_dpiC * dYp / dLy) -
dLy * dLy / 3 - 0.5 * dLy * dLy / (m_dpiC * m_dpiC)));
double dExpDecay = exp(-(log(dEta) / m_dbC) * (log(dEta) / m_dbC));
double dRefProfile1 = log(dEta);
double dRefProfile2 = 2 / (m_dbC * m_dbC) * log(dEta) * log(dEta) - 1.0;
// Total geopotential distribution
dGeopotential = dAvgGeopotential + dXYGeopotential*
dRefProfile1 * dExpDecay;
// Total temperature distribution
dTemperature = dAvgTemperature + dXYGeopotential / dRd *
dRefProfile2 * dExpDecay;
}
Material::ChemicalFormula
Material::parseChemicalFormula(const std::string chemicalSymbol) {
Material::ChemicalFormula CF;
tokenizer tokens(chemicalSymbol, " -",
Mantid::Kernel::StringTokenizer::TOK_IGNORE_EMPTY);
for (auto atom = tokens.begin(); atom != tokens.end(); ++atom) {
try {
std::string name(*atom);
float numberAtoms = 1;
uint16_t aNumber = 0;
// split out the isotope bit
if (atom->find('(') != std::string::npos) {
// error check
size_t end = atom->find(')');
if (end == std::string::npos) {
std::stringstream msg;
msg << "Failed to parse isotope \"" << name << "\"";
throw std::runtime_error(msg.str());
}
// get the number of atoms
std::string numberAtomsStr = name.substr(end + 1);
if (!numberAtomsStr.empty())
numberAtoms = boost::lexical_cast<float>(numberAtomsStr);
// split up the atom and isotope number
name = name.substr(1, end - 1);
str_pair temp = getAtomName(name);
name = temp.first;
aNumber = boost::lexical_cast<uint16_t>(temp.second);
} else // for non-isotopes
{
str_pair temp = getAtomName(name);
name = temp.first;
if (!temp.second.empty())
numberAtoms = boost::lexical_cast<float>(temp.second);
}
CF.atoms.push_back(boost::make_shared<Atom>(getAtom(name, aNumber)));
CF.numberAtoms.push_back(numberAtoms);
} catch (boost::bad_lexical_cast &e) {
std::stringstream msg;
msg << "While trying to parse atom \"" << (*atom)
<< "\" encountered bad_lexical_cast: " << e.what();
throw std::runtime_error(msg.str());
}
}
return CF;
}
/// <summary>
/// Evaluate the reference state at the given point.
/// </summary>
virtual void EvaluateReferenceState(
const PhysicalConstants & phys,
double dZp,
double dXp,
double dYp,
double * dState
) const {
const double dLy = m_dGDim[3] - m_dGDim[2];
// Pressure coordinate
double dGeopotential;
double dTemperature;
double dEta = EtaFromRLL(
phys, dZp, dXp, dYp, dGeopotential, dTemperature);
// Calculate zonal velocity and set other velocity components
double dExpDecay = exp(-(log(dEta) / m_dbC) * (log(dEta) / m_dbC));
double dUlon =
-m_dU0 * sin(m_dpiC * dYp / dLy) * sin(m_dpiC * dYp / dLy) *
log(dEta) * dExpDecay;
dState[0] = dUlon;
dState[1] = 0.0;
dState[3] = 0.0;
// Calculate rho and theta
double dPressure = phys.GetP0() * dEta;
//std::cout << std::setprecision(16) << "Z = " << dZp << " Eta = " << dEta << "\n";
double dRho = dPressure / (phys.GetR() * dTemperature);
double dRhoTheta = phys.RhoThetaFromPressure(dPressure);
dState[2] = dRhoTheta / dRho;
dState[4] = dRho;
}
/// <summary>
/// Evaluate the state vector at the given point.
/// </summary>
virtual void EvaluatePointwiseState(
const PhysicalConstants & phys,
const Time & time,
double dZp,
double dXp,
double dYp,
double * dState,
double * dTracer
) const {
const double dG = phys.GetG();
const double dCv = phys.GetCv();
const double dCp = phys.GetCp();
const double dRd = phys.GetR();
const double dP0 = phys.GetP0();
// Base potential temperature field
double dThetaBar = m_dTheta0 * exp(m_dNbar * m_dNbar / dG * dZp);
// Set the uniform U, V, W field for all time
dState[0] = m_dU0;
dState[1] = 0.0;
dState[3] = 0.0;
dState[3] = sin(M_PI * dZp / m_dGDim[5]);
// Set the initial density based on the Exner pressure
double dExnerP = (dG * dG) / (dCp * m_dTheta0 * m_dNbar * m_dNbar);
dExnerP *= (exp(-m_dNbar * m_dNbar / dG * dZp) - 1.0);
dExnerP += 1.0;
double dRho = dP0 / (dRd * dThetaBar) * pow(dExnerP,(dCv / dRd));
dState[4] = dRho;
// Set the initial theta field
//dState[2] = phys.PressureFromRhoTheta(dThetaBar * dRho);
//dState[2] = (dThetaBar * dRho);
dState[2] = dThetaBar;
}
/// <summary>
/// Obtain test case specific physical constants.
/// </summary>
virtual void EvaluatePhysicalConstants(
PhysicalConstants & phys
) const {
// No Coriolis
phys.SetOmega(0.0);
}
/// <summary>
/// Evaluate the state vector at the given point.
/// </summary>
virtual void EvaluatePointwiseState(
const PhysicalConstants & phys,
const Time & time,
double dZ,
double dLon,
double dLat,
double * dState,
double * dTracer
) const {
// Radius
double dR = dZ + phys.GetEarthRadius();
// Calculate parameters
double dT0 = 0.5 * (ParamT0E + ParamT0P);
double dConstA = 1.0 / ParamLapseRate;
double dConstB = (dT0 - ParamT0P) / (dT0 * ParamT0P);
double dConstC = 0.5 * (ParamK + 2.0)
* (ParamT0E - ParamT0P) / (ParamT0E * ParamT0P);
double dConstH = phys.GetR() * dT0 / phys.GetG();
// Computed quantities
double dScaledZ = dZ / (ParamB * dConstH);
// Calculate tau values
double dTau1 =
dConstA * ParamLapseRate / dT0
* exp(ParamLapseRate / dT0 * dZ)
+ dConstB
* (1.0 - 2.0 * dScaledZ * dScaledZ)
* exp(- dScaledZ * dScaledZ);
double dTau2 =
dConstC * (1.0 - 2.0 * dScaledZ * dScaledZ)
* exp(- dScaledZ * dScaledZ);
double dIntTau1 =
dConstA * (exp(ParamLapseRate / dT0 * dZ) - 1.0)
+ dConstB * dZ * exp(- dScaledZ * dScaledZ);
double dIntTau2 =
dConstC * dZ * exp(- dScaledZ * dScaledZ);
// Calculate utility terms
double dRRatio;
if (m_fDeepAtmosphere) {
dRRatio = dR / phys.GetEarthRadius();
} else {
dRRatio = 1.0;
}
double dInteriorTerm = pow(dRRatio * cos(dLat), ParamK)
- ParamK / (ParamK + 2.0) * pow(dRRatio * cos(dLat), ParamK + 2.0);
// Calculate temperature
double dTemperature = 1.0
/ (dRRatio * dRRatio)
/ (dTau1 - dTau2 * dInteriorTerm);
// Calculate hydrostatic pressure
double dPressure = phys.GetP0() * exp(
- phys.GetG() / phys.GetR()
* (dIntTau1 - dIntTau2 * dInteriorTerm));
// Calculate hydrostatic density
double dRho = dPressure / (phys.GetR() * dTemperature);
// Velocity field
double dInteriorTermU =
pow(dRRatio * cos(dLat), ParamK - 1.0)
- pow(dRRatio * cos(dLat), ParamK + 1.0);
double dBigU = phys.GetG() / phys.GetEarthRadius() * ParamK
* dIntTau2 * dInteriorTermU * dTemperature;
double dRCosLat;
if (m_fDeepAtmosphere) {
dRCosLat = dR * cos(dLat);
} else {
dRCosLat = phys.GetEarthRadius() * cos(dLat);
}
double dOmegaRCosLat = phys.GetOmega() * dRCosLat;
if (dOmegaRCosLat * dOmegaRCosLat + dRCosLat * dBigU < 0.0) {
_EXCEPTIONT("Negative discriminant detected.");
}
double dUlon = - dOmegaRCosLat +
sqrt(dOmegaRCosLat * dOmegaRCosLat + dRCosLat * dBigU);
double dUlat = 0.0;
// Calculate velocity perturbation
double dUlonPert;
double dUlatPert;
EvaluatePointwisePerturbation(
phys, dZ, dLon, dLat,
dUlonPert, dUlatPert);
dUlon += dUlonPert;
dUlat += dUlatPert;
// Store the state
dState[0] = dUlon;
dState[1] = dUlat;
dState[2] = phys.RhoThetaFromPressure(dPressure) / dRho;
dState[3] = 0.0;
dState[4] = dRho;
}
/// <summary>
/// Evaluate the reference state at the given point.
/// </summary>
virtual void EvaluateReferenceState(
const PhysicalConstants & phys,
double dZ,
double dLon,
double dLat,
double * dState
) const {
// Radius
double dR = dZ + phys.GetEarthRadius();
// Calculate parameters
double dT0 = 0.5 * (ParamT0E + ParamT0P);
double dConstA = 1.0 / ParamLapseRate;
double dConstB = (dT0 - ParamT0P) / (dT0 * ParamT0P);
double dConstC = 0.5 * (ParamK + 2.0)
* (ParamT0E - ParamT0P) / (ParamT0E * ParamT0P);
double dConstH = phys.GetR() * dT0 / phys.GetG();
// Computed quantities
double dScaledZ = dZ / (ParamB * dConstH);
// Calculate tau values
double dTau1 =
dConstA * ParamLapseRate / dT0
* exp(ParamLapseRate / dT0 * dZ)
+ dConstB
* (1.0 - 2.0 * dScaledZ * dScaledZ)
* exp(- dScaledZ * dScaledZ);
double dTau2 =
dConstC * (1.0 - 2.0 * dScaledZ * dScaledZ)
* exp(- dScaledZ * dScaledZ);
double dIntTau1 =
dConstA * (exp(ParamLapseRate / dT0 * dZ) - 1.0)
+ dConstB * dZ * exp(- dScaledZ * dScaledZ);
double dIntTau2 =
dConstC * dZ * exp(- dScaledZ * dScaledZ);
// Calculate utility terms
double dRRatio;
if (m_fDeepAtmosphere) {
dRRatio = dR / phys.GetEarthRadius();
} else {
dRRatio = 1.0;
}
double dInteriorTerm = pow(dRRatio * cos(dLat), ParamK)
- ParamK / (ParamK + 2.0) * pow(dRRatio * cos(dLat), ParamK + 2.0);
// Calculate temperature
double dTemperature = 1.0
/ (dRRatio * dRRatio)
/ (dTau1 - dTau2 * dInteriorTerm);
// Calculate hydrostatic pressure
double dPressure = phys.GetP0() * exp(
- phys.GetG() / phys.GetR()
* (dIntTau1 - dIntTau2 * dInteriorTerm));
/*
// Calculate pressure derivative
double dDrPressure;
if (m_fDeepAtmosphere) {
dDrPressure =
dPressure * phys.GetG() / phys.GetR() * (
- dTau1 + dTau2 * dInteriorTerm
+ dIntTau2 * ParamK / dR
* (pow(dRRatio * cos(dLat), ParamK)
- pow(dRRatio * cos(dLat), ParamK + 2.0)));
} else {
dDrPressure =
dPressure * phys.GetG() / phys.GetR() * (
- dTau1 + dTau2 * dInteriorTerm);
}
// Calculate hydrostatic density
double dHydroRho = - dRRatio * dRRatio / phys.GetG() * dDrPressure;
*/
// Calculate exact density
double dRho = dPressure / (phys.GetR() * dTemperature);
// Store the state
dState[0] = 0.0;
dState[1] = 0.0;
dState[2] = phys.RhoThetaFromPressure(dPressure) / dRho;
dState[3] = 0.0;
dState[4] = dRho;
}
/// <summary>
/// Obtain test case specific physical constants.
/// </summary>
virtual void EvaluatePhysicalConstants(
PhysicalConstants & phys
) const {
// Set the alpha parameter
phys.SetAlpha(m_dAlpha);
}
/// <summary>
/// Obtain test case specific physical constants.
/// </summary>
virtual void EvaluatePhysicalConstants(
PhysicalConstants & phys
) const {
phys.SetOmega(m_dOmega * m_dEarthScaling);
phys.SetEarthRadius(phys.GetEarthRadius() / m_dEarthScaling);
}
