CGFields::StandardFields Class Reference

Contains the computed field values, like density, momentum and stress. More...

#include <StandardFields.h>

Inheritance diagram for CGFields::StandardFields:

Public Member Functions
	StandardFields ()
	Default constructor, sets all field values to zero. More...
	StandardFields (const StandardFields &P)=default
	Default copy constructor, copies the values of all fields. More...
	~StandardFields ()=default
	Destructor, it simply destructs the StandardFields and all the objects it contains. More...
void	write (std::ostream &os) const
	Writes class content into an output stream, typically a stat file. More...
void	output (std::ostream &os) const
	Writes human-readable class content into an output stream, typically a stat file. More...
void	setZero ()
	Sets all fields to zero. More...
StandardFields	getSquared () const
	Returns the square of all field values (to calculate standard deviation). More...
StandardFields &	operator= (const StandardFields &P)
	Copies all field values. More...
StandardFields &	operator+= (const StandardFields &P)
	Adds the field values on the RHS to the LHS of the equation. More...
StandardFields &	operator-= (const StandardFields &P)
	Subtracts the field values on the RHS from the LHS of the equation. More...
StandardFields &	operator/= (Mdouble a)
	Divides the field values on the LHS by the RHS of the equation. More...
StandardFields	operator* (Mdouble a) const
	Multiplies the field values on the left of the '*' by the scalar value on the right of the '*' and returns the answer. More...
void	addParticleStatistics (Mdouble phi, const StandardFields &currentInteraction)
	This function should be called from within a loop over all particles to compute all the fields that are defined as a sum over all particles (e.g. density, momentum). More...
void	addParticleDifferentialStatistics (Vec3D &dphi, const StandardFields &currentInteraction)
void	addInteractionStatistics (Mdouble psi, const StandardFields &currentInteraction)
	This function should be called from within a loop over all Interactions to compute all the fields that are defined as a sum over all Interactions (e.g. stress). More...
void	addContactPointStatistics (Mdouble phi, const StandardFields &currentInteraction)
	This function should be called from within a loop over all Interactions to compute all the fields that are defined as a sum over all Interactions with external objects (e.g. IFD). More...
void	setFields (const BaseInteraction &c, IntegralType type)
void	setCylindricalFields (const BaseInteraction &c, IntegralType type)
void	setFields (const BaseParticle &p)
void	setCylindricalFields (const BaseParticle &p)
Mdouble	getVolumeFraction () const
Mdouble	getDensity () const
Vec3D	getMomentum () const
MatrixSymmetric3D	getMomentumFlux () const
Matrix3D	getContactStress () const
Vec3D	getInteractionForceDensity () const
Mdouble	getParticleSizeDensity (size_t i) const
std::array< Mdouble, 6 >	getParticleSizeDensity () const
std::array< Mdouble, 6 >	getParticleSizeMomenta () const
std::array< Mdouble, 6 >	getCentralParticleSizeMomenta () const
std::array< Mdouble, 6 >	getStandardisedParticleSizeMomenta () const
void	outputStandardisedParticleSizeMomenta (std::ostream &os) const

Static Public Member Functions
static void	writeNames (std::ostream &os, unsigned countVariables)
static bool	doInteractionStatistics ()
	Returns true if the class contains fields that are defined as a sum over all Interactions (e.g. stress), else returns false. More...
static bool	evaluateFixedParticles ()
static bool	isDifferentialField ()

Private Attributes
Mdouble	volumeFraction_
Mdouble	density_
Vec3D	momentum_
MatrixSymmetric3D	momentumFlux_
Matrix3D	contactStress_
Vec3D	interactionForceDensity_
std::array< Mdouble, 6 >	particleSizeDensity_

Detailed Description

Contains the computed field values, like density, momentum and stress.

CGPoints inherits from this class; CGPoints::evaluate adds to the values of these variables.

Todo:

These are currently the only fields that are computed. However, this class is destined to be extended to contain additional information such as fabric, energy, local angular momentum. Also, a simpler version is planned, where only particle statistics are evaluated (density and momentum).

Constructor & Destructor Documentation

StandardFields() [1/2]

CGFields::StandardFields::StandardFields

(

)

Default constructor, sets all field values to zero.

{
    setZero();
#ifdef DEBUG_CONSTRUCTOR
    std::cerr << "StandardFields::StandardFields() finished" << std::endl;
#endif
}

References setZero().

StandardFields() [2/2]

CGFields::StandardFields::StandardFields ( const StandardFields &  P )

default

Default copy constructor, copies the values of all fields.

~StandardFields()

CGFields::StandardFields::~StandardFields ( )

default

Destructor, it simply destructs the StandardFields and all the objects it contains.

Member Function Documentation

addContactPointStatistics()

void CGFields::StandardFields::addContactPointStatistics	(	Mdouble	phi,
		const StandardFields &	currentInteraction
	)

This function should be called from within a loop over all Interactions to compute all the fields that are defined as a sum over all Interactions with external objects (e.g. IFD).

Parameters

[in]	phi	the value of the cg function for the contact point of c and the current CGPoint
[in]	c	the interaction which is used in the cg function

{
    interactionForceDensity_ += currentInteraction.getInteractionForceDensity() * phi;
}

References getInteractionForceDensity(), and interactionForceDensity_.

addInteractionStatistics()

void CGFields::StandardFields::addInteractionStatistics	(	Mdouble	psi,
		const StandardFields &	currentInteraction
	)

This function should be called from within a loop over all Interactions to compute all the fields that are defined as a sum over all Interactions (e.g. stress).

Parameters

[in]	psi	the value of the line integral from C to P at the current CGPoint
[in]	c	the contact which is used in the line integral

{
    contactStress_ += currentInteraction.getContactStress() * psi;
}

References contactStress_, and getContactStress().

addParticleDifferentialStatistics()

void CGFields::StandardFields::addParticleDifferentialStatistics	(	Vec3D &	dphi,
		const StandardFields &	currentInteraction
	)

{
}

addParticleStatistics()

void CGFields::StandardFields::addParticleStatistics	(	Mdouble	phi,
		const StandardFields &	currentInteraction
	)

This function should be called from within a loop over all particles to compute all the fields that are defined as a sum over all particles (e.g. density, momentum).

Parameters

[in]	phi	the value of the cg function at the current CGPoint
[in]	currentInteraction	the fields which are produced due to the particle at its centre

{
    volumeFraction_ += currentInteraction.getVolumeFraction() * phi;
    density_ += currentInteraction.getDensity() * phi;
    momentum_ += currentInteraction.getMomentum() * phi;
    momentumFlux_ += currentInteraction.getMomentumFlux() * phi;
    for (size_t i = 0; i < particleSizeDensity_.size(); ++i)
        particleSizeDensity_[i] += currentInteraction.getParticleSizeDensity(i) * phi;
}

References density_, getDensity(), getMomentum(), getMomentumFlux(), getParticleSizeDensity(), getVolumeFraction(), constants::i, momentum_, momentumFlux_, particleSizeDensity_, and volumeFraction_.

doInteractionStatistics()

bool CGFields::StandardFields::doInteractionStatistics ( )

static

Returns true if the class contains fields that are defined as a sum over all Interactions (e.g. stress), else returns false.

If the functions returns false, addInteractionStatistics and addContactPointStatistics are never called.

Returns

True if the class contains fields that are defined as a sum over all Interactions, else false.

{
    return true;
}

evaluateFixedParticles()

static bool CGFields::StandardFields::evaluateFixedParticles ( )

inlinestatic

    {
        return false;
    }

getCentralParticleSizeMomenta()

std::array< Mdouble, 6 > CGFields::StandardFields::getCentralParticleSizeMomenta

(

)

const

{
    //https://en.wikipedia.org/wiki/Central_moment
    auto momenta = getParticleSizeMomenta();
    Mdouble mean = momenta[1];
    momenta[5] += -5 * mean * momenta[4] + 10 * mean * mean * momenta[3]
                  - 10 * mean * mean * mean * momenta[2] + 4 * mean * mean * mean * mean * mean;
    momenta[4] += -4 * mean * momenta[3] + 6 * mean * mean * momenta[2] - 3 * mean * mean * mean * mean;
    momenta[3] += -3 * mean * momenta[2] + 2 * mean * mean * mean;
    momenta[2] += -mean * mean;
    return momenta;
}

References getParticleSizeMomenta().

Referenced by getStandardisedParticleSizeMomenta().

getContactStress()

Matrix3D CGFields::StandardFields::getContactStress ( ) const

inline

    {
        return contactStress_;
    }

References contactStress_.

Referenced by addInteractionStatistics().

getDensity()

Mdouble CGFields::StandardFields::getDensity ( ) const

inline

    {
        return density_;
    }

References density_.

Referenced by addParticleStatistics(), and testCGHandler().

getInteractionForceDensity()

Vec3D CGFields::StandardFields::getInteractionForceDensity ( ) const

inline

    {
        return interactionForceDensity_;
    }

References interactionForceDensity_.

Referenced by addContactPointStatistics(), and testCGHandler().

getMomentum()

Vec3D CGFields::StandardFields::getMomentum ( ) const

inline

    {
        return momentum_;
    }

References momentum_.

Referenced by addParticleStatistics().

getMomentumFlux()

MatrixSymmetric3D CGFields::StandardFields::getMomentumFlux ( ) const

inline

    {
        return momentumFlux_;
    }

References momentumFlux_.

Referenced by addParticleStatistics().

getParticleSizeDensity() [1/2]

std::array<Mdouble, 6> CGFields::StandardFields::getParticleSizeDensity ( ) const

inline

    {
        return particleSizeDensity_;
    }

References particleSizeDensity_.

getParticleSizeDensity() [2/2]

Mdouble CGFields::StandardFields::getParticleSizeDensity ( size_t  i ) const

inline

    {
        return particleSizeDensity_[i];
    }

References constants::i, and particleSizeDensity_.

Referenced by addParticleStatistics().

getParticleSizeMomenta()

std::array< Mdouble, 6 > CGFields::StandardFields::getParticleSizeMomenta

(

)

const

{
    //https://en.wikipedia.org/wiki/Moment_(mathematics)
    auto momenta = particleSizeDensity_;
    for (size_t i = 1; i < particleSizeDensity_.size(); ++i)
    {
        momenta[i] /= particleSizeDensity_[0];
    }
    return momenta;
}

References constants::i, and particleSizeDensity_.

Referenced by getCentralParticleSizeMomenta().

getSquared()

StandardFields CGFields::StandardFields::getSquared

(

)

const

Returns the square of all field values (to calculate standard deviation).

Returns

a CGField containing the square of the values in the current object

{
    StandardFields P;
    P.volumeFraction_ = mathsFunc::square(volumeFraction_);
    P.density_ = mathsFunc::square(density_);
    P.momentum_ = Vec3D::square(momentum_);
    P.momentumFlux_ = MatrixSymmetric3D::square(momentumFlux_);
    P.contactStress_ = Matrix3D::square(contactStress_);
    P.interactionForceDensity_ = Vec3D::square(interactionForceDensity_);
    P.particleSizeDensity_ = particleSizeDensity_;
    for (auto& p : P.particleSizeDensity_) p *= p;
    return P;
}

References contactStress_, density_, interactionForceDensity_, momentum_, momentumFlux_, Global_Physical_Variables::P, particleSizeDensity_, Matrix3D::square(), MatrixSymmetric3D::square(), mathsFunc::square(), Vec3D::square(), and volumeFraction_.

getStandardisedParticleSizeMomenta()

std::array< Mdouble, 6 > CGFields::StandardFields::getStandardisedParticleSizeMomenta

(

)

const

{
    auto momenta = getCentralParticleSizeMomenta();
    Mdouble std = std::sqrt(momenta[2]);
    momenta[3] /= std * std * std;
    momenta[4] /= std * std * std * std;
    momenta[5] /= std * std * std * std * std;
    return momenta;
}

References getCentralParticleSizeMomenta().

Referenced by outputStandardisedParticleSizeMomenta().

getVolumeFraction()

Mdouble CGFields::StandardFields::getVolumeFraction ( ) const

inline

    {
        return volumeFraction_;
    }

References volumeFraction_.

Referenced by addParticleStatistics().

isDifferentialField()

static bool CGFields::StandardFields::isDifferentialField ( )

inlinestatic

A bool that determines if the derivative of the CG function has to be computed

    {
        return false;
    }

operator*()

StandardFields CGFields::StandardFields::operator*

(

Mdouble

a

)

const

Multiplies the field values on the left of the '*' by the scalar value on the right of the '*' and returns the answer.

Parameters

[in]

a

the scalar that we multiply with

Returns

the CGField to which the multiplied values are written

{
    StandardFields p;
    p.volumeFraction_ = volumeFraction_ * a;
    p.density_ = density_ * a;
    p.momentum_ = momentum_ * a;
    p.momentumFlux_ = momentumFlux_ * a;
    p.contactStress_ = contactStress_ * a;
    p.interactionForceDensity_ = interactionForceDensity_ * a;
    for (size_t i = 0; i < particleSizeDensity_.size(); ++i)
        p.particleSizeDensity_[i] = particleSizeDensity_[i] * a;
    return p;
}

References contactStress_, density_, constants::i, interactionForceDensity_, momentum_, momentumFlux_, particleSizeDensity_, and volumeFraction_.

operator+=()

StandardFields & CGFields::StandardFields::operator+=

(

const StandardFields &

P

)

Adds the field values on the RHS to the LHS of the equation.

Parameters

[in]

P

the CGField that has to be added

Returns

the CGField to which the values are added

{
    volumeFraction_ += P.volumeFraction_;
    density_ += P.density_;
    momentum_ += P.momentum_;
    momentumFlux_ += P.momentumFlux_;
    contactStress_ += P.contactStress_;
    interactionForceDensity_ += P.interactionForceDensity_;
    for (size_t i = 0; i < particleSizeDensity_.size(); ++i) particleSizeDensity_[i] += P.particleSizeDensity_[i];
    return *this;
}

References contactStress_, density_, constants::i, interactionForceDensity_, momentum_, momentumFlux_, Global_Physical_Variables::P, particleSizeDensity_, and volumeFraction_.

operator-=()

StandardFields & CGFields::StandardFields::operator-=

(

const StandardFields &

P

)

Subtracts the field values on the RHS from the LHS of the equation.

Parameters

[in]

P

the CGField that has to be subtracted

Returns

the CGField from which the values are subtracted

{
    volumeFraction_ -= P.volumeFraction_;
    density_ -= P.density_;
    momentum_ -= P.momentum_;
    momentumFlux_ -= P.momentumFlux_;
    contactStress_ -= P.contactStress_;
    interactionForceDensity_ -= P.interactionForceDensity_;
    for (size_t i = 0; i < particleSizeDensity_.size(); ++i) particleSizeDensity_[i] -= P.particleSizeDensity_[i];
    return *this;
}

References contactStress_, density_, constants::i, interactionForceDensity_, momentum_, momentumFlux_, Global_Physical_Variables::P, particleSizeDensity_, and volumeFraction_.

operator/=()

StandardFields & CGFields::StandardFields::operator/=

(

Mdouble

a

)

Divides the field values on the LHS by the RHS of the equation.

Parameters

[in]

a

the scalar that we divide by

Returns

the CGField to which the divided values are written

{
    volumeFraction_ /= a;
    density_ /= a;
    momentum_ /= a;
    momentumFlux_ /= a;
    contactStress_ /= a;
    interactionForceDensity_ /= a;
    for (auto& p : particleSizeDensity_) p /= a;
    return *this;
}

References contactStress_, density_, interactionForceDensity_, momentum_, momentumFlux_, particleSizeDensity_, and volumeFraction_.

operator=()

StandardFields & CGFields::StandardFields::operator= ( const StandardFields &  P )

default

Copies all field values.

Parameters

[in]

P

the CGField that has to be copied

Returns

the CGField into which the values are copied

output()

void CGFields::StandardFields::output

(

std::ostream &

os

)

const

Writes human-readable class content into an output stream, typically a stat file.

Parameters

[in,out]

os

the ostream into which the data is written.

{
    os << "VolumeFraction " << volumeFraction_;
    os << " Density " << density_;
    os << " Momentum " << momentum_;
    os << " MomentumFlux " << momentumFlux_;
    os << " ContactStress " << contactStress_;
    os << " InteractionForce " << interactionForceDensity_;
    os << " ParticleSize";
    for (const auto p : particleSizeDensity_) os << ' ' << p;
}

References contactStress_, density_, interactionForceDensity_, momentum_, momentumFlux_, particleSizeDensity_, and volumeFraction_.

outputStandardisedParticleSizeMomenta()

void CGFields::StandardFields::outputStandardisedParticleSizeMomenta

(

std::ostream &

os

)

const

{
    //https://en.wikipedia.org/wiki/Moment_%28mathematics%29#Higher_moments
    auto momenta = getStandardisedParticleSizeMomenta();
    os << "Particle number: " << momenta[0] << '\n';
    os << "Mean radius: " << momenta[1] << '\n';
    os << "Standard deviation: " << std::sqrt(momenta[2]) << '\n';
    os << "Skewness: " << momenta[3] << '\n'; //left- or right-sided
    os << "Kurtosis: " << momenta[4] << '\n'; //heavy or light tailed (3 for normal distribution)
    os << "5-th moment: " << momenta[5] << '\n'; //hyper skewness (0 for normal dist)
}

References getStandardisedParticleSizeMomenta().

setCylindricalFields() [1/2]

void CGFields::StandardFields::setCylindricalFields	(	const BaseInteraction &	c,
		IntegralType	type
	)

{
    setFields(c, type);
    contactStress_ = contactStress_.getCylindricalTensorField(c.getContactPoint());
    interactionForceDensity_ = interactionForceDensity_.getCylindricalTensorField(c.getContactPoint());
}

References contactStress_, BaseInteraction::getContactPoint(), Matrix3D::getCylindricalTensorField(), Vec3D::getCylindricalTensorField(), interactionForceDensity_, and setFields().

setCylindricalFields() [2/2]

void CGFields::StandardFields::setCylindricalFields

(

const BaseParticle &

p

)

{
    setFields(p);
    momentum_ = momentum_.getCylindricalTensorField(p.getPosition());
    momentumFlux_ = momentumFlux_.getCylindricalTensorField(p.getPosition());
}

References MatrixSymmetric3D::getCylindricalTensorField(), Vec3D::getCylindricalTensorField(), BaseInteractable::getPosition(), momentum_, momentumFlux_, and setFields().

setFields() [1/2]

void CGFields::StandardFields::setFields	(	const BaseInteraction &	c,
		IntegralType	type
	)

{
    //P is always real, but I not
    if (type == IntegralType::I_TO_P)
    {
        contactStress_ = Matrix3D::dyadic(c.getForce(), c.getIP());
    }
    else if (type == IntegralType::I_TO_CONTACT)
    {
        contactStress_ = Matrix3D::dyadic(c.getForce(), c.getIC());
    }
    else
    {
        contactStress_ = Matrix3D::dyadic(c.getForce(), c.getCP());
    }
    interactionForceDensity_ = c.getForce();
}

References contactStress_, Matrix3D::dyadic(), BaseInteraction::getCP(), BaseInteraction::getForce(), BaseInteraction::getIC(), BaseInteraction::getIP(), I_TO_CONTACT, I_TO_P, and interactionForceDensity_.

Referenced by setCylindricalFields().

setFields() [2/2]

void CGFields::StandardFields::setFields

(

const BaseParticle &

p

)

{
    volumeFraction_ = p.getVolume();
    density_ = p.getMass();
    momentum_ = p.getVelocity() * p.getMass();
    momentumFlux_ = MatrixSymmetric3D::selfDyadic(p.getVelocity()) * p.getMass();
    Mdouble particleSize = 1.0;
    for (auto& ps : particleSizeDensity_)
    {
        ps = particleSize;
        particleSize *= p.getRadius();
    }
}

References density_, BaseParticle::getMass(), BaseParticle::getRadius(), BaseInteractable::getVelocity(), BaseParticle::getVolume(), momentum_, momentumFlux_, particleSizeDensity_, MatrixSymmetric3D::selfDyadic(), and volumeFraction_.

setZero()

void CGFields::StandardFields::setZero

(

)

Sets all fields to zero.

{
    volumeFraction_ = 0.0;
    density_ = 0.0;
    momentum_.setZero();
    momentumFlux_.setZero();
    contactStress_.setZero();
    interactionForceDensity_.setZero();
    for (auto& p : particleSizeDensity_) p = 0;
}

References contactStress_, density_, interactionForceDensity_, momentum_, momentumFlux_, particleSizeDensity_, Matrix3D::setZero(), MatrixSymmetric3D::setZero(), Vec3D::setZero(), and volumeFraction_.

Referenced by StandardFields().

write()

void CGFields::StandardFields::write

(

std::ostream &

os

)

const

Writes class content into an output stream, typically a stat file.

Parameters

[in,out]

os

the ostream into which the data is written.

{
    os << volumeFraction_;
    os << ' ' << density_;
    os << ' ' << momentum_;
    os << ' ' << momentumFlux_;
    os << ' ' << contactStress_;
    os << ' ' << interactionForceDensity_;
    for (const auto p : particleSizeDensity_) os << ' ' << p;
}

References contactStress_, density_, interactionForceDensity_, momentum_, momentumFlux_, particleSizeDensity_, and volumeFraction_.

writeNames()

void CGFields::StandardFields::writeNames ( std::ostream &  os, unsigned  countVariables  )

static

Parameters

[in,out]	os	the ostream into which the data is written.
[in]	countVariables	The number of variables in the field (including time), e.g. 1 for O, 4 for XYZ

{
    os << countVariables + 1 << ":VolumeFraction "; //volume
    os << countVariables + 2 << ":Density "; //mass
    os << countVariables + 3 << '-' << countVariables + 5 << ":Momentum ";
    os << countVariables + 6 << '-' << countVariables + 11 << ":MomentumFlux ";
    os << countVariables + 12 << '-' << countVariables + 20 << ":ContactStress ";
    os << countVariables + 21 << '-' << countVariables + 23 << ":InteractionForce ";
    os << countVariables + 24 << '-' << countVariables + 29 << ":ParticleSize ";
}

Member Data Documentation

contactStress_

Matrix3D CGFields::StandardFields::contactStress_

private

Contact stress, computed as the sum over all contacts between particle i and particle/wall/fixed particle j

\[\mathbf \sigma^{c}(\vec r,t)=\sum_{ij} \vec f_{ij} \otimes \vec l_{ij} \psi(\vec r,\vec r_i,\vec r_j),\]

with contact force \(\vec f_{ij}\), branch vector \(\vec l_{ij}= \vec c_{ij}-\vec r_i\), particle position \(\vec r_i\), contact point \(\vec c_{ij}\), and cg line integral \(\psi(\vec r,\vec r_i,\vec r_j)\), see CGFunctions::Gauss::evaluateCGIntegral.

Referenced by addInteractionStatistics(), getContactStress(), getSquared(), operator*(), operator+=(), operator-=(), operator/=(), output(), setCylindricalFields(), setFields(), setZero(), and write().

density_

Mdouble CGFields::StandardFields::density_

private

(Mass) density, computed as the sum over all particles i

\[\rho(\vec r,t)=\sum_i m_i \phi(\vec r,\vec r_i)\]

with particle mass m_i and cg function \(\phi(\vec r,\vec r_i),\), see CGFunctions::Gauss::evaluateCGFunction.

Referenced by addParticleStatistics(), getDensity(), getSquared(), operator*(), operator+=(), operator-=(), operator/=(), output(), setFields(), setZero(), and write().

interactionForceDensity_

Vec3D CGFields::StandardFields::interactionForceDensity_

private

Interaction force density, computed as the sum over all contacts between particle i and (external) wall/fixed particle j

\[\vec{IFD}(\vec r,t)=\sum_{ij} f_{ij} \phi(\vec r,\vec c_{ij}),\]

with contact force \(\vec f_{ij}\) and cg function \(\phi(\vec r,\vec r_i)\), see CGFunctions::Gauss::evaluateCGFunction.

Referenced by addContactPointStatistics(), getInteractionForceDensity(), getSquared(), operator*(), operator+=(), operator-=(), operator/=(), output(), setCylindricalFields(), setFields(), setZero(), and write().

momentum_

Vec3D CGFields::StandardFields::momentum_

private

Momentum, computed as the sum over all particles i

\[\vec j(\vec r,t)=\sum_i m_i \vec v_i\phi(\vec r,\vec r_i),\]

with particle momentum \(m_i\vec v_i\) and cg function \(\phi(\vec r,\vec r_i)\), see CGFunctions::Gauss::evaluateCGFunction.

Velocity can be calculated in a post-processing step from momentum and density as

\[\vec V(\vec r,t) = \frac{\vec j(\vec r,t)}{\rho(\vec r,t)}.\]

Referenced by addParticleStatistics(), getMomentum(), getSquared(), operator*(), operator+=(), operator-=(), operator/=(), output(), setCylindricalFields(), setFields(), setZero(), and write().

momentumFlux_

MatrixSymmetric3D CGFields::StandardFields::momentumFlux_

private

Momentum, computed as the sum over all particles i

\[\mathbf k(\vec r,t)=\sum_i m_i \vec v_i \otimes \vec v_i\phi(\vec r,\vec r_i),\]

with particle momentum flux \(m_i\vec v_i \otimes \vec v_i\) and cg function \(\phi(\vec r,\vec r_i)\), see CGFunctions::Gauss::evaluateCGFunction.

Kinetic stress can be calculated in a post-processing step from momentum flux and density as

\[\mathbf \sigma^{k} = \mathbf k - \rho \vec V \otimes \vec V.\]

Referenced by addParticleStatistics(), getMomentumFlux(), getSquared(), operator*(), operator+=(), operator-=(), operator/=(), output(), setCylindricalFields(), setFields(), setZero(), and write().

particleSizeDensity_

std::array<Mdouble, 6> CGFields::StandardFields::particleSizeDensity_

private

Density of particle size, and powers of particle size,

\[ \vec{PS}_k(\vec r,t)= \sum_i r_i^k \phi(\vec r),\]

with radius \(r_i\).

Used to compute the first five moments of the particle size distribution,

\[ <r^k>(\vec r,t)= \vec{PS}_k / \vec{PS}_0, \]

with \(\vec{PS}_0\) denoting the number density.

Referenced by addParticleStatistics(), getParticleSizeDensity(), getParticleSizeMomenta(), getSquared(), operator*(), operator+=(), operator-=(), operator/=(), output(), setFields(), setZero(), and write().

volumeFraction_

Mdouble CGFields::StandardFields::volumeFraction_

private

Particle volume fraction, computed as the sum over all particles i

\[\nu(\vec r,t)=\sum_i V_i \phi(\vec r,\vec r_i),\]

with particle volume V_i and cg function \(\phi(\vec r,\vec r_i)\), see CGFunctions::Gauss::evaluateCGFunction.

Referenced by addParticleStatistics(), getSquared(), getVolumeFraction(), operator*(), operator+=(), operator-=(), operator/=(), output(), setFields(), setZero(), and write().

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The documentation for this class was generated from the following files:

• StandardFields.h
• StandardFields.cc