Continuum model for the 3D heat equation with exponential decay $\partial_t u = \nabla D \nabla u - \mu u$ . More...

#include <euler_grid.h>

Inheritance diagram for bdm::EulerGrid:

Collaboration diagram for bdm::EulerGrid:

Public Member Functions
	EulerGrid ()=default

	EulerGrid (int substance_id, std::string substance_name, real_t dc, real_t mu, int resolution=10)

void	DiffuseWithClosedEdge (real_t dt) override

void	DiffuseWithOpenEdge (real_t dt) override

void	DiffuseWithDirichlet (real_t dt) override

void	DiffuseWithNeumann (real_t dt) override

void	DiffuseWithPeriodic (real_t dt) override

Public Member Functions inherited from bdm::DiffusionGrid
	DiffusionGrid ()=default

	DiffusionGrid (const TRootIOCtor *)

	DiffusionGrid (int substance_id, const std::string &substance_name, real_t dc, real_t mu, int resolution=10)

	~DiffusionGrid () override=default

	DiffusionGrid (const DiffusionGrid &)=delete

DiffusionGrid &	operator= (const DiffusionGrid &)=delete

	DiffusionGrid (DiffusionGrid &&)=delete

DiffusionGrid &	operator= (DiffusionGrid &&)=delete

void	Initialize () override

void	Update () override

void	Step (real_t dt) override

void	Diffuse (real_t dt)

void	CalculateGradient ()

void	RunInitializers ()

void	ChangeConcentrationBy (const Real3 &position, real_t amount, InteractionMode mode=InteractionMode::kAdditive, bool scale_with_resolution=false)

void	ChangeConcentrationBy (size_t idx, real_t amount, InteractionMode mode=InteractionMode::kAdditive, bool scale_with_resolution=false)
	See ChangeConcentrationBy(const Real3&, real_t, InteractionMode, bool). More...

real_t	GetValue (const Real3 &position) const override
	Get the value of the scalar field at specified position. More...

real_t	GetConcentration (const Real3 &position) const

real_t	GetConcentration (const size_t idx) const
	Get the concentration at specified index. More...

Real3	GetGradient (const Real3 &position) const override

virtual void	GetGradient (const Real3 &position, Real3 *gradient, bool normalize=true) const

std::array< uint32_t, 3 >	GetBoxCoordinates (const Real3 &position) const
	Get the coordinates of the box at the specified position. More...

std::array< uint32_t, 3 >	GetBoxCoordinates (const size_t idx) const

size_t	GetBoxIndex (const std::array< uint32_t, 3 > &box_coord) const
	Calculates the box index at specified box coordinates. More...

size_t	GetBoxIndex (const Real3 &position) const
	Calculates the box index of the substance at specified position. More...

std::array< size_t, 6 >	GetNeighboringBoxes (size_t index) const

std::array< size_t, 6 >	GetNeighboringBoxes (size_t index, const std::array< uint32_t, 3 > &box_coord) const

void	SetDecayConstant (real_t mu)

real_t	GetLastTimestep () const
	Return the last timestep `dt` that was used to run `Diffuse(dt)` More...

void	SetUpperThreshold (real_t t)

real_t	GetUpperThreshold () const

void	SetLowerThreshold (real_t t)

real_t	GetLowerThreshold () const

const real_t *	GetAllConcentrations () const

const real_t *	GetAllGradients () const

std::array< size_t, 3 >	GetNumBoxesArray () const

size_t	GetNumBoxes () const

real_t	GetBoxLength () const

int	GetSubstanceId () const

const std::string &	GetSubstanceName () const

real_t	GetDecayConstant () const

const int32_t *	GetDimensionsPtr () const

std::array< int32_t, 6 >	GetDimensions () const

std::array< int32_t, 3 >	GetGridSize () const

const std::array< real_t, 7 > &	GetDiffusionCoefficients () const

size_t	GetResolution () const

real_t	GetBoxVolume () const

template<typename F >
void	AddInitializer (F function)

bool	IsFixedSubstance ()
	Return if a substance is stationary, e.g. (mu == 0 && dc == 0) More...

void	SetBoundaryCondition (std::unique_ptr< BoundaryCondition > bc)
	Set the boundary condition, takes ownership of the object. More...

BoundaryCondition *	GetBoundaryCondition () const
	Returns the boundary condition. Does not transfer ownership. More...

void	SetBoundaryConditionType (BoundaryConditionType bc_type)
	Sets boundary condition type. More...

BoundaryConditionType	GetBoundaryConditionType () const
	Returns the BoundaryConditionType, see `BoundaryConditionType` More...

void	PrintInfo (std::ostream &out=std::cout)
	Print information about the Diffusion Grid. More...

void	PrintInfoWithInitialization ()
	Print the information after initialization. More...

bool	IsInitialized () const
	Returns if the grid has been initialized. More...

void	TurnOffGradientCalculation ()

Public Member Functions inherited from bdm::ScalarField
	ScalarField ()=default

	ScalarField (const TRootIOCtor *)

	~ScalarField () override=default

	BDM_CLASS_DEF_OVERRIDE (ScalarField, 1)

Public Member Functions inherited from bdm::Continuum
	Continuum ()=default

	Continuum (const TRootIOCtor *)

virtual	~Continuum ()=default

void	IntegrateTimeAsynchronously (real_t dt)

int	GetContinuumId () const
	Returns the ID of the continuum. More...

void	SetContinuumId (int id)
	Sets the ID of the continuum. More...

const std::string &	GetContinuumName () const
	Returns the name of the continuum. More...

void	SetContinuumName (const std::string &name)
	Sets the name of the continuum. More...

real_t	GetSimulatedTime () const
	Returns the time simulated by the continuum. More...

void	SetTimeStep (real_t dt)

real_t	GetTimeStep () const
	Returns the time step for the continuum. More...

Private Member Functions
	BDM_CLASS_DEF_OVERRIDE (EulerGrid, 1)

Detailed Description

Continuum model for the 3D heat equation with exponential decay $\partial_t u = \nabla D \nabla u - \mu u$ .

We use a forward in time and central in space finite difference method for modelling (FTCS). This method, however, is not iherently stable and thus we must impose a stability condition. $\frac{D \Delta t}{\Delta x^2} < \frac{1}{6}$ . The error of this method scaling linearly with time (forward difference of first-order) and quadratic with the spatial discretization (central difference of second-order). The method derives its name, Euler, from the time step length of the integration.

Further information:

Definition at line 43 of file euler_grid.h.

Constructor & Destructor Documentation

◆ EulerGrid() [1/2]

bdm::EulerGrid::EulerGrid ( )

default

◆ EulerGrid() [2/2]

bdm::EulerGrid::EulerGrid	(	int	substance_id,
		std::string	substance_name,
		real_t	dc,
		real_t	mu,
		int	resolution = `10`
	)

inline

Definition at line 46 of file euler_grid.h.

Member Function Documentation

◆ BDM_CLASS_DEF_OVERRIDE()

bdm::EulerGrid::BDM_CLASS_DEF_OVERRIDE	(	EulerGrid	,
		1
	)

private

◆ DiffuseWithClosedEdge()

void bdm::EulerGrid::DiffuseWithClosedEdge ( real_t dt )

overridevirtual

Implements bdm::DiffusionGrid.

Definition at line 21 of file euler_grid.cc.

◆ DiffuseWithDirichlet()

void bdm::EulerGrid::DiffuseWithDirichlet ( real_t dt )

overridevirtual

Compute the diffusion of the substance with Dirichlet boundary conditions ( u = const on the boundary) for a given time step dt.

Implements bdm::DiffusionGrid.

Definition at line 157 of file euler_grid.cc.

◆ DiffuseWithNeumann()

void bdm::EulerGrid::DiffuseWithNeumann ( real_t dt )

overridevirtual

Compute the diffusion of the substance with Neumann boundary conditions (du/dn = const on the boundary) for a given time step dt.

Implements bdm::DiffusionGrid.

Definition at line 213 of file euler_grid.cc.

◆ DiffuseWithOpenEdge()

void bdm::EulerGrid::DiffuseWithOpenEdge ( real_t dt )

overridevirtual

Implements bdm::DiffusionGrid.

Definition at line 69 of file euler_grid.cc.

◆ DiffuseWithPeriodic()

void bdm::EulerGrid::DiffuseWithPeriodic ( real_t dt )

overridevirtual

Compute the diffusion of the substance with Periodic boundary conditions (u_{-1} = {u_N-1}, u_{N} = u_{0}) for a given time step dt.

Implements bdm::DiffusionGrid.

Definition at line 304 of file euler_grid.cc.

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

core/diffusion/euler_grid.h
core/diffusion/euler_grid.cc

Public Member Functions

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ EulerGrid() [1/2]

◆ EulerGrid() [2/2]

Member Function Documentation

◆ BDM_CLASS_DEF_OVERRIDE()

◆ DiffuseWithClosedEdge()

◆ DiffuseWithDirichlet()

◆ DiffuseWithNeumann()

◆ DiffuseWithOpenEdge()

◆ DiffuseWithPeriodic()