aspect::VolumeOfFluid::Utilities Namespace Reference

Functions
double	compute_fluid_fraction (const Tensor< 1, 2 > normal, const double d)
double	compute_fluid_fraction (const Tensor< 1, 3 > normal, const double d)
double	compute_interface_location (const Tensor< 1, 2 > normal, const double volume_fraction)
double	compute_interface_location (const Tensor< 1, 3 > normal, const double volume_fraction)
void	xFEM_Heaviside (const unsigned int degree, const Tensor< 1, 2 > normal, const double d, const std::vector< Point< 2 >> &points, std::vector< double > &values)
void	xFEM_Heaviside (const unsigned int degree, const Tensor< 1, 3 > normal, const double d, const std::vector< Point< 3 >> &points, std::vector< double > &values)
void	xFEM_Heaviside_derivative_d (const unsigned int degree, const Tensor< 1, 2 > normal, const double d, const std::vector< Point< 2 >> &points, std::vector< double > &values)
void	xFEM_Heaviside_derivative_d (const unsigned int degree, const Tensor< 1, 3 > normal, const double d, const std::vector< Point< 3 >> &points, std::vector< double > &values)
template<int dim>
double	compute_interface_location_newton (const unsigned int degree, const Tensor< 1, dim, double > normal, const double volume_fraction, const double vol, const double epsilon, const std::vector< Point< dim >> &points, const std::vector< double > &weights)
template<int dim>
double	compute_fluid_volume (const unsigned int degree, const Tensor< 1, dim, double > normal, const double d, const std::vector< Point< dim >> &points, const std::vector< double > &weights)
template<int dim>
double	calculate_volume_flux (const unsigned int compute_direction, const double time_direction_derivative, const Tensor< 1, dim, double > interface_normal_in_cell, const double d_at_face_center)

Function Documentation

compute_fluid_fraction() [1/2]

double aspect::VolumeOfFluid::Utilities::compute_fluid_fraction	(	const Tensor< 1, 2 >	normal,
		const double	d
	)

Function to calculate volume fraction contained by indicator function H(d-normal*(x'-x_{cen}')) on the [0, 1]^dim unit cell where x_{cen} is the unit cell center.

Currently only works assuming constant Jacobian determinant.

compute_fluid_fraction() [2/2]

double aspect::VolumeOfFluid::Utilities::compute_fluid_fraction	(	const Tensor< 1, 3 >	normal,
		const double	d
	)

compute_interface_location() [1/2]

double aspect::VolumeOfFluid::Utilities::compute_interface_location	(	const Tensor< 1, 2 >	normal,
		const double	volume_fraction
	)

Function to calculate required value of d to obtain given volume fraction for indicator function H(d-normal*(x'-x_{cen}')) on the [0, 1]^dim unit cell where x_{cen} is the unit cell center.

Currently only works assuming constant Jacobian determinant.

compute_interface_location() [2/2]

double aspect::VolumeOfFluid::Utilities::compute_interface_location	(	const Tensor< 1, 3 >	normal,
		const double	volume_fraction
	)

xFEM_Heaviside() [1/2]

void aspect::VolumeOfFluid::Utilities::xFEM_Heaviside	(	const unsigned int	degree,
		const Tensor< 1, 2 >	normal,
		const double	d,
		const std::vector< Point< 2 >> &	points,
		std::vector< double > &	values
	)

Obtain values at points for a polynomial function that is equivalent to the Heaviside function \(H(d-normal*xhat)\) on the unit cell when integrated against polynomials of up to the specified degree.

Currently works for degree <=1

Parameters

degree	Maximum degree for exact integration
normal	Interface normal vector, pointed away from the included region
d	Interface parameter specifying location of interface in unit cell
points	Locations to evaluate the constructed polynomial
values	Values of the constructed polynomial at the specified points

xFEM_Heaviside() [2/2]

void aspect::VolumeOfFluid::Utilities::xFEM_Heaviside	(	const unsigned int	degree,
		const Tensor< 1, 3 >	normal,
		const double	d,
		const std::vector< Point< 3 >> &	points,
		std::vector< double > &	values
	)

xFEM_Heaviside_derivative_d() [1/2]

void aspect::VolumeOfFluid::Utilities::xFEM_Heaviside_derivative_d	(	const unsigned int	degree,
		const Tensor< 1, 2 >	normal,
		const double	d,
		const std::vector< Point< 2 >> &	points,
		std::vector< double > &	values
	)

Obtain values at points for a polynomial function that is equivalent to the function \(\frac{d}{dd}H(d-normal*xhat)\) on the unit cell when integrated against polynomials of up to the specified degree.

Currently works for degree <=1

Parameters

degree	Maximum degree for exact integration
normal	Interface normal vector, pointed away from the included region
d	Interface parameter specifying location of interface in unit cell
points	Locations to evaluate the constructed polynomial
values	Values of the constructed polynomial at the specified points

xFEM_Heaviside_derivative_d() [2/2]

void aspect::VolumeOfFluid::Utilities::xFEM_Heaviside_derivative_d	(	const unsigned int	degree,
		const Tensor< 1, 3 >	normal,
		const double	d,
		const std::vector< Point< 3 >> &	points,
		std::vector< double > &	values
	)

compute_interface_location_newton()

template<int dim>

double aspect::VolumeOfFluid::Utilities::compute_interface_location_newton	(	const unsigned int	degree,
		const Tensor< 1, dim, double >	normal,
		const double	volume_fraction,
		const double	vol,
		const double	epsilon,
		const std::vector< Point< dim >> &	points,
		const std::vector< double > &	weights
	)

Function to do Newton iteration calculation of correct d for a given normal to get volume_fraction from xFEM_Heaviside integrated against the given weights.

Parameters

degree	Maximum degree for exact integration
normal	Interface normal vector, pointed away from the included region
volume_fraction	Cell volume fraction in physical space - used for target value for integration
vol	Cell volume in physical space - used for target value for integration
epsilon	Tolerance for Newton iteration
points	Quadrature points to use for update
weights	JxW values to use for quadrature

compute_fluid_volume()

template<int dim>

double aspect::VolumeOfFluid::Utilities::compute_fluid_volume	(	const unsigned int	degree,
		const Tensor< 1, dim, double >	normal,
		const double	d,
		const std::vector< Point< dim >> &	points,
		const std::vector< double > &	weights
	)

Function to calculate volume contained by indicator function \(H(d-normal*(x'-x_{cen}'))\) on the \([0, 1]^dim\) unit cell where \(x_{cen}\) is the unit cell center, using a polynomial mapping of degree up to "degree".

Parameters

degree	Maximum degree for exact integration
normal	Interface normal vector, pointed away from the included region
d	Interface parameter specifying location of interface in unit cell by distance from cell center
points	Quadrature points to use for update
weights	JxW values to use for quadrature

calculate_volume_flux()

template<int dim>

double aspect::VolumeOfFluid::Utilities::calculate_volume_flux	(	const unsigned int	compute_direction,
		const double	time_direction_derivative,
		const Tensor< 1, dim, double >	interface_normal_in_cell,
		const double	d_at_face_center
	)

Function to calculate flux volume fraction based on a method of characteristics approximation of the interface on the cell's face over the timestep. Calculation assumes an approximation to the interface of the form \(H(d-normal*(x'-x_{face center})-time_direction_derivative*t')\) where \(t'\) is in terms of a "unit timestep".

Parameters

compute_direction	Dimension of unit cell we are currently computing along
time_direction_derivative	Approximated gradient in time for the "level set" describing the interface.
interface_normal_in_cell	The normal vector for the current interface reconstruction in the computing cell.
d_at_face_center	The correct d value to for the interface description on the face we are computing for.