TVDReconstructor< dim_, Limiter, NumberType > Class Template Reference#

DiFfRG: DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType > Class Template Reference

DiFfRG

Discretization Framework for functional Renormalization Group flows

TVD gradient reconstructor parameterised by a slope limiter. More...

#include <tvd_reconstructor.hh>

Public Types
using	LimiterType = Limiter

Static Public Member Functions
template<int n_components>
static GradientType< dim, NumberType, n_components >	compute_gradient (const dealii::Point< dim > &center_pos, const std::array< NumberType, n_components > &u_center, const std::array< dealii::Point< dim >, n_faces > &x_n, const std::array< std::array< NumberType, n_components >, n_faces > &u_n)
	Compute the gradient of u using the injected slope limiter.

template<int n_components>
static GradientType< dim, NumberType, n_components >	compute_gradient_at_point (const dealii::Point< dim > &center_pos, const dealii::Point< dim > &x, const std::array< NumberType, n_components > &u_center, const std::array< dealii::Point< dim >, n_faces > &x_n, const std::array< std::array< NumberType, n_components >, n_faces > &u_n)

template<int n_components>
static GradientType< dim, NumberType, n_components >	compute_gradient_derivative (const dealii::Point< dim > &center_pos, const std::array< ADNumberType, n_components > &u_center, const std::array< dealii::Point< dim >, n_faces > &x_n, const std::array< std::array< ADNumberType, n_components >, n_faces > &u_n)
	Compute the derivative of the limited gradient w.r.t. a single stencil DOF.

template<int n_components>
static GradientType< dim, NumberType, n_components >	compute_gradient_at_point_derivative (const dealii::Point< dim > &center_pos, const dealii::Point< dim > &x, const std::array< ADNumberType, n_components > &u_center, const std::array< dealii::Point< dim >, n_faces > &x_n, const std::array< std::array< ADNumberType, n_components >, n_faces > &u_n)

template<int n_components>
static ThirdDerivativeType< dim, NumberType, n_components >	compute_third_derivatives_at_face (const std::array< dealii::Point< dim >, 4 > &x_stencil, const std::array< std::array< NumberType, n_components >, 4 > &u_stencil)

template<int n_components>
static ThirdDerivativeType< dim, NumberType, n_components >	compute_third_derivatives_at_face_derivative (const std::array< dealii::Point< dim >, 4 > &x_stencil, const std::array< std::array< ADNumberType, n_components >, 4 > &u_stencil)

Static Public Attributes
static constexpr int	dim = dim_

static constexpr int	n_faces = 2 * dim

static constexpr int	jacobian_stencil_radius = 2

Private Types
using	ADNumberType = autodiff::Real<1, NumberType>

Detailed Description

template<int dim_, HasSlopeLimiter Limiter, typename NumberType>
class DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >

TVD gradient reconstructor parameterised by a slope limiter.

Computes piecewise-linear cell gradients on a rectangular mesh using two one-sided finite-difference slopes per dimension, each pair limited by the injected Limiter.

When the limiter satisfies the TVD property (e.g. MinModLimiter), the resulting reconstruction is Total Variation Diminishing.

Template Parameters

dim	The spatial dimension of the reconstruction.
Limiter	A type satisfying the `HasSlopeLimiter` concept (e.g. `MinModLimiter`).
NumberType	The numeric type used for computations (e.g. `double`, `float`).

Usage with the KT assembler:

using Assembler = FV::KurganovTadmor::Assembler<

Discretization, Model, def::TVDReconstructor<Discretization::dim, def::MinModLimiter, double>>;

DiFfRG::FV::KurganovTadmor::Assembler

Definition KurganovTadmor.hh:645

DiFfRG::def::TVDReconstructor

TVD gradient reconstructor parameterised by a slope limiter.

Definition tvd_reconstructor.hh:46

Member Typedef Documentation

◆ ADNumberType

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

using DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::ADNumberType = autodiff::Real<1, NumberType>

private

◆ LimiterType

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

using DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::LimiterType = Limiter

Member Function Documentation

◆ compute_gradient()

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

template<int n_components>

static GradientType< dim, NumberType, n_components > DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::compute_gradient	(	const dealii::Point< dim > &	center_pos,
		const std::array< NumberType, n_components > &	u_center,
		const std::array< dealii::Point< dim >, n_faces > &	x_n,
		const std::array< std::array< NumberType, n_components >, n_faces > &	u_n )

inlinestatic

Compute the gradient of u using the injected slope limiter.

For every component and every spatial dimension the method computes two one-sided slopes from the cell centre to its axis-aligned neighbours and returns the limiter-processed gradient.

Template Parameters

n_components the number of components in u

Parameters

center_pos	position of the cell centre
u_center	solution values at the cell centre
x_n	positions of the def::n_faces<dim> neighbouring cell centres, ordered as pairs (left, right) for dim 0, then dim 1, …
u_n	solution values at those neighbours

Returns: per-component gradient vector

◆ compute_gradient_at_point()

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

template<int n_components>

static GradientType< dim, NumberType, n_components > DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::compute_gradient_at_point	(	const dealii::Point< dim > &	center_pos,
		const dealii::Point< dim > &	x,
		const std::array< NumberType, n_components > &	u_center,
		const std::array< dealii::Point< dim >, n_faces > &	x_n,
		const std::array< std::array< NumberType, n_components >, n_faces > &	u_n )

inlinestatic

◆ compute_gradient_at_point_derivative()

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

template<int n_components>

static GradientType< dim, NumberType, n_components > DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::compute_gradient_at_point_derivative	(	const dealii::Point< dim > &	center_pos,
		const dealii::Point< dim > &	x,
		const std::array< ADNumberType, n_components > &	u_center,
		const std::array< dealii::Point< dim >, n_faces > &	x_n,
		const std::array< std::array< ADNumberType, n_components >, n_faces > &	u_n )

inlinestatic

◆ compute_gradient_derivative()

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

template<int n_components>

static GradientType< dim, NumberType, n_components > DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::compute_gradient_derivative	(	const dealii::Point< dim > &	center_pos,
		const std::array< ADNumberType, n_components > &	u_center,
		const std::array< dealii::Point< dim >, n_faces > &	x_n,
		const std::array< std::array< ADNumberType, n_components >, n_faces > &	u_n )

inlinestatic

Compute the derivative of the limited gradient w.r.t. a single stencil DOF.

The inputs are already seeded autodiff::Real<1,NumberType> values; exactly one entry across u_center and u_n should have a non-zero derivative part (set via seed()).

Unlike compute_gradient, this method does not evaluate the reconstruction at a face point — it returns the per-component derivative of the gradient itself.

Template Parameters

n_components the number of solution components

Parameters

center_pos	position of the cell centre
u_center	cell-centre values as seeded AD types
x_n	positions of the def::n_faces<dim> neighbouring cell centres
u_n	neighbour values as seeded AD types

Returns: per-component gradient-derivative tensor d(grad u_c) / d(u_target)

◆ compute_third_derivatives_at_face()

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

template<int n_components>

static ThirdDerivativeType< dim, NumberType, n_components > DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::compute_third_derivatives_at_face	(	const std::array< dealii::Point< dim >, 4 > &	x_stencil,
		const std::array< std::array< NumberType, n_components >, 4 > &	u_stencil )

inlinestatic

◆ compute_third_derivatives_at_face_derivative()

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

template<int n_components>

static ThirdDerivativeType< dim, NumberType, n_components > DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::compute_third_derivatives_at_face_derivative	(	const std::array< dealii::Point< dim >, 4 > &	x_stencil,
		const std::array< std::array< ADNumberType, n_components >, 4 > &	u_stencil )

inlinestatic

Member Data Documentation

◆ dim

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

int DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::dim = dim_

staticconstexpr

◆ jacobian_stencil_radius

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

int DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::jacobian_stencil_radius = 2

staticconstexpr

◆ n_faces

template<int dim_, HasSlopeLimiter Limiter, typename NumberType >

int DiFfRG::def::TVDReconstructor< dim_, Limiter, NumberType >::n_faces = 2 * dim

staticconstexpr

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

/home/runner/work/DiFfRG_current/DiFfRG_current/DiFfRG/include/DiFfRG/discretization/FV/reconstructor/advection/tvd_reconstructor.hh

TVDReconstructor&lt; dim_, Limiter, NumberType &gt; Class Template Reference#

Public Types

Static Public Member Functions

Static Public Attributes

Private Types

Detailed Description

Member Typedef Documentation

◆ ADNumberType

◆ LimiterType

Member Function Documentation

◆ compute_gradient()

◆ compute_gradient_at_point()

◆ compute_gradient_at_point_derivative()

◆ compute_gradient_derivative()

◆ compute_third_derivatives_at_face()

◆ compute_third_derivatives_at_face_derivative()

Member Data Documentation

◆ dim

◆ jacobian_stencil_radius

◆ n_faces

TVDReconstructor< dim_, Limiter, NumberType > Class Template Reference#