Diamond difference approximation in one dimension. More...

Inheritance diagram for DD1D:

Collaboration diagram for DD1D:

Public Member Functions
function	DD1D (in mesh, in mat, in quadrature)
	Class constructor.
function	get_con_x (in obj, in octant)
function	setup_group (in obj, in group)
	Setup the equations for a group.
function	setup_octant (in obj, in octant)
	Setup the equations for an octant.
function	setup_angle (in obj, in mu)
	Setup the equations for an angle.
function	solve (in obj, in g, in psi_in, in s, in i)
	Solve for the cell-center and outgoing edge fluxes.
Public Attributes
Property	d_con_x
Property	d_sig
Property	d_beta
Constant Property	HORZ = 1
Constant Property	VERT = 2
Protected Attributes
Property	d_mesh
	Problem mesh.
Property	d_mat
	Material definitions.
Property	d_quadrature
	Quadrature.
Property	d_mu
	Current mu value.
Property	d_eta
	current eta value
Property	d_ksi
	Current ksi value.
Property	d_alpha
	Weighted diamond difference parameter.
Property	d_mat_map
	Material map.

Detailed Description

Diamond difference approximation in one dimension.

The 1-D discretized transport equation in

$|\mu_n| (\psi_{i,n,out} - \psi_{i,n,in}) + \Delta \Sigma \psi_{i,n} = \Delta Q_{i, n} \, .$

To solve this, the cell center flux is related to the incoming and outgoing edge fluxes by a general relation

$\psi_{i,n} = \frac{1+\alpha_{i,n}}{2}\psi_{i,n,out} + \frac{1-\alpha_{i,n}}{2}\psi_{i,n,in} \, .$

Solving for the outgoing flux and inserting in the transport equation yields

$\psi_{i,n} = \frac{Q_{i,n} + \psi_{i,n,in} \frac{2\mu}{\Delta(\alpha_{i,n}+1)}} {\frac{2\mu}{\Delta(\alpha_{i,n}+1)} + \Sigma} \, ,$

and

$\psi_{i,n,out} = \frac{2}{\alpha_{i,n}+1}\psi_{i,n} + \frac{\alpha_{i,n}-1}{\alpha_{i,n}+1} \psi_{i,n,in} \, .$

For the diamond difference approximation, $\alpha = 0$ over all indices.

In general, we define

$con_{x,i,n} = \frac{2\mu}{\Delta(\alpha_{i,n}+1)} ,$

$\beta{1} = \frac{2}{\alpha_{i,n}+1} \, ,$

and

$\beta{2} = \frac{\alpha_{i,n}-1}{\alpha_{i,n}+1} \, .$

which applies to other discretizations, thus yielding a consistent interface.

See also:: SD1D

Constructor & Destructor Documentation

function DD1D	(	in	mesh,
		in	mat,
		in	quadrature
	)

Class constructor.

Set the mesh and material.

Parameters:

mesh	Problem mesh.
mat	Material definitions.

Returns:: Instance of the DD1D class.

Member Function Documentation

function get_con_x	(	in	obj,
		in	octant
	)

function setup_angle	(	in	obj,
		in	mu
	)

Setup the equations for an angle.

Parameters:

mu	Cosine with respect to x axis.
eta	Cosine with respect to y axis.

function setup_group	(	in	obj,
		in	group
	)

Setup the equations for a group.

Here, we'll go through the grid and produce a fine mesh matrix of total cross-sections. This isn't the best thing for memory, but it cuts down a lot on the time within solve.

Parameters:

group Current group.

function setup_octant	(	in	obj,
		in	octant
	)

Setup the equations for an octant.

Parameters:

octant Current octant.

function solve	(	in	obj,
		in	g,
		in	psi_in,
		in	s,
		in	i
	)

Solve for the cell-center and outgoing edge fluxes.

Parameters:

g	Group index
psi_in	Incident flux vector
s	Cell source
i	Cell x index

Returns:: Cell center angular flux and outgoing edge fluxes.

Member Data Documentation

Property d_alpha [protected, inherited]

Weighted diamond difference parameter.

Property d_beta

Property d_con_x

Property d_eta [protected, inherited]

current eta value

Property d_ksi [protected, inherited]

Current ksi value.

Property d_mat [protected, inherited]

Material definitions.

Property d_mat_map [protected, inherited]

Material map.

Property d_mesh [protected, inherited]

Problem mesh.

Property d_mu [protected, inherited]

Current mu value.

Property d_quadrature [protected, inherited]

Quadrature.

Property d_sig

Constant Property HORZ = 1 [inherited]

Constant Property VERT = 2 [inherited]

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

/home/robertsj/Research/matlab_transport_pack/source/DD1D.m

DD1D Class Reference

Public Member Functions

Public Attributes

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation