DiffusionSystem Class Reference

System representing diffusion of a single solution component. More...

#include <diffusionSystem.h>

Inheritance diagram for DiffusionSystem:

Public Member Functions
	DiffusionSystem ()
void	get_A (dvec &a, dvec &b, dvec &c)
	Build the matrix A describing the linear ODE.
void	get_k (dvec &k)
	Provides the constant term k to the integrator.
void	resize (size_t N)
	Set the number of points in the domain.
void	resetSplitConstants ()
	Set the splitting constant C to zero.
Public Member Functions inherited from TridiagonalODE
	TridiagonalODE ()
virtual	~TridiagonalODE ()
virtual void	get_A (dvec &a, dvec &b, dvec &c)=0
	Provide the matrix associated with the ODE to the integrator.
virtual void	get_k (dvec &k)=0
	Provides the constant term k to the integrator.
virtual void	resize (size_t N)
	Set the number of points in the domain.
virtual void	initialize ()
Public Member Functions inherited from GridBased
	GridBased ()
virtual	~GridBased ()
virtual void	setGrid (const OneDimGrid &grid)
	Copy the specified grid to this object.

Public Attributes
dvec	B
	scaling factor for the spatial derivative
dvec	D
	diffusion coefficient or equivalent
dvec	splitConst
	Balancing constant introduced by the splitting method.
size_t	N
	Number of points in the region to be solved.
double	yInf
	reference value for wall flux boundary condition
double	wallConst
	wall flux proportionality constant
Public Attributes inherited from GridBased
OneDimGrid	grid
	the actual grid

Private Attributes
dvec	c1
dvec	c2

Additional Inherited Members
Protected Attributes inherited from GridBased
dvec &	x
	The coordinates of the grid points [m].
dvec &	r
	"radius" at x[j].
dvec &	rphalf
	"radius" at x[j+1/2].
dvec &	hh
	Grid spacing between x[j] and x[j+1].
dvec &	dlj
	Average of left and right grid spacing.
dvec &	cfm
	Coefficient for y[j-1] in first centered difference.
dvec &	cf
	Coefficient for y[j] in first centered difference.
dvec &	cfp
	Coefficient for y[j+1] in first centered difference.
int &	alpha
	curved grid exponent.
int &	beta
	curved grid exponent.
size_t &	nPoints
	number of grid point
size_t &	jj
	index of last grid point (== nPoints-1)

Detailed Description

System representing diffusion of a single solution component.

Represents an ODE in one of the following forms:

\[ \dot{y} = B \frac{d}{dx}\left(D \frac{dy}{dx}\right) + C \]

\[ \dot{y} = \frac{B}{r} \frac{d}{dr}\left(r D \frac{dy}{dr}\right) + C \]

The ODE in this form may be written as a linear system:

\[ \dot{y} = Ay + k \]

where the entries of the matrix A are determined by the prefactor B, the diffusion coefficients D, the boundary conditions and the finite difference formulas used.

Constructor & Destructor Documentation

DiffusionSystem()

DiffusionSystem::DiffusionSystem

(

)

Member Function Documentation

get_A()

void DiffusionSystem::get_A ( dvec &  a, dvec &  b, dvec &  c  )

virtual

Build the matrix A describing the linear ODE.

a[j], b[j], and c[j] are respectivley the subdiagonal, diagonal, and superdiagonal elements of row j.

Implements TridiagonalODE.

get_k()

void DiffusionSystem::get_k ( dvec &  k )

virtual

Provides the constant term k to the integrator.

Implements TridiagonalODE.

resize()

void DiffusionSystem::resize ( size_t  N )

virtual

Set the number of points in the domain.

Reimplemented from TridiagonalODE.

resetSplitConstants()

void DiffusionSystem::resetSplitConstants

(

)

Set the splitting constant C to zero.

Member Data Documentation

B

dvec DiffusionSystem::B

scaling factor for the spatial derivative

D

dvec DiffusionSystem::D

diffusion coefficient or equivalent

splitConst

dvec DiffusionSystem::splitConst

Balancing constant introduced by the splitting method.

N

size_t DiffusionSystem::N

Number of points in the region to be solved.

yInf

double DiffusionSystem::yInf

reference value for wall flux boundary condition

wallConst

double DiffusionSystem::wallConst

wall flux proportionality constant

c1

dvec DiffusionSystem::c1

private

c2

dvec DiffusionSystem::c2

private

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

• src/diffusionSystem.h
• src/diffusionSystem.cpp