IntegralRayKernel

Description

IntegralRayKernel is the base class for integrating a quantity $var element = document.getElementById("moose-equation-8d153444-8238-4713-a90c-db879dc7a24d");katex.render("f(r)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ along a Ray and accumulating the integral into a data member on the Ray. The integral computed is:

var element = document.getElementById("moose-equation-98ceb4f4-c1da-4cfc-a661-2bc08b35b19a");katex.render("\\int_L f(r)~dr, \\quad L = \\{\\vec{r}_1 + t\\vec{r}_2 \\mid t \\in [0, 1]\\}\\,,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-5677aeac-c120-47d3-94ba-572cd6fe1239");katex.render("f(r)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is integrated from $var element = document.getElementById("moose-equation-b332226b-6dbe-427d-98f1-cca5bd6bc435");katex.render("\\vec{r}_1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ to $var element = document.getElementById("moose-equation-baa13faf-69ff-401d-8f49-27306cddb0de");katex.render("\\vec{r}_2", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

note

IntegralRayKernel is not to be used for contributing to a residual or Jacobian along a Ray. For this case, you should derive from RayKernel or ADRayKernel.

For examples, see:

VariableIntegralRayKernel for integrating a Variable or an AuxVariable
MaterialIntegralRayKernel for integrating a Material
FunctionIntegralRayKernel for integrating a Function

To integrate along a desired quantity, inherit from IntegralRayKernel and override the computeQpIntegral() method in which _qp is the current quadrature point index. For example:

Real
VariableIntegralRayKernel::computeQpIntegral()
{
  return _u[_qp];
}

Many other useful member variables exist that describe the Ray segment. For more information, see Using a RayKernel.

The integrated value produced by a class that derives from this should be obtained using the RayIntegralValue postprocessor. For example:

[RayKernels<<<{"href": "../../syntax/RayKernels/index.html"}>>>]
  [variable_integral]
    type = VariableIntegralRayKernel<<<{"description": "Integrates a Variable or AuxVariable along a Ray.", "href": "VariableIntegralRayKernel.html"}>>>
    study<<<{"description": "The RayTracingStudy associated with this object. If none provided, this will default to the one study that exists."}>>> = study
    variable<<<{"description": "The name of the variable to integrate"}>>> = u
  []
  [aux_variable_integral]
    type = VariableIntegralRayKernel<<<{"description": "Integrates a Variable or AuxVariable along a Ray.", "href": "VariableIntegralRayKernel.html"}>>>
    study<<<{"description": "The RayTracingStudy associated with this object. If none provided, this will default to the one study that exists."}>>> = study
    variable<<<{"description": "The name of the variable to integrate"}>>> = aux
  []
[]

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [diag_value]
    type = RayIntegralValue<<<{"description": "Obtains the integrated value accumulated into a Ray from an IntegralRayKernel-derived class.", "href": "../postprocessors/RayIntegralValue.html"}>>>
    ray_kernel<<<{"description": "The name of the IntegralRayKernel-derived RayKernel to obtain the integral value of"}>>> = variable_integral
    ray<<<{"description": "Name of the Ray to get the final integral value from"}>>> = diag
  []
  [top_across_value]
    type = RayIntegralValue<<<{"description": "Obtains the integrated value accumulated into a Ray from an IntegralRayKernel-derived class.", "href": "../postprocessors/RayIntegralValue.html"}>>>
    ray_kernel<<<{"description": "The name of the IntegralRayKernel-derived RayKernel to obtain the integral value of"}>>> = variable_integral
    ray<<<{"description": "Name of the Ray to get the final integral value from"}>>> = top_across
  []
  [bottom_across_value]
    type = RayIntegralValue<<<{"description": "Obtains the integrated value accumulated into a Ray from an IntegralRayKernel-derived class.", "href": "../postprocessors/RayIntegralValue.html"}>>>
    ray_kernel<<<{"description": "The name of the IntegralRayKernel-derived RayKernel to obtain the integral value of"}>>> = variable_integral
    ray<<<{"description": "Name of the Ray to get the final integral value from"}>>> = bottom_across
  []
  [partial_value]
    type = RayIntegralValue<<<{"description": "Obtains the integrated value accumulated into a Ray from an IntegralRayKernel-derived class.", "href": "../postprocessors/RayIntegralValue.html"}>>>
    ray_kernel<<<{"description": "The name of the IntegralRayKernel-derived RayKernel to obtain the integral value of"}>>> = variable_integral
    ray<<<{"description": "Name of the Ray to get the final integral value from"}>>> = partial
  []

  [aux_diag_value]
    type = RayIntegralValue<<<{"description": "Obtains the integrated value accumulated into a Ray from an IntegralRayKernel-derived class.", "href": "../postprocessors/RayIntegralValue.html"}>>>
    ray_kernel<<<{"description": "The name of the IntegralRayKernel-derived RayKernel to obtain the integral value of"}>>> = aux_variable_integral
    ray<<<{"description": "Name of the Ray to get the final integral value from"}>>> = diag
  []
  [aux_top_across_value]
    type = RayIntegralValue<<<{"description": "Obtains the integrated value accumulated into a Ray from an IntegralRayKernel-derived class.", "href": "../postprocessors/RayIntegralValue.html"}>>>
    ray_kernel<<<{"description": "The name of the IntegralRayKernel-derived RayKernel to obtain the integral value of"}>>> = aux_variable_integral
    ray<<<{"description": "Name of the Ray to get the final integral value from"}>>> = top_across
  []
  [aux_bottom_across_value]
    type = RayIntegralValue<<<{"description": "Obtains the integrated value accumulated into a Ray from an IntegralRayKernel-derived class.", "href": "../postprocessors/RayIntegralValue.html"}>>>
    ray_kernel<<<{"description": "The name of the IntegralRayKernel-derived RayKernel to obtain the integral value of"}>>> = aux_variable_integral
    ray<<<{"description": "Name of the Ray to get the final integral value from"}>>> = bottom_across
  []
  [aux_partial_value]
    type = RayIntegralValue<<<{"description": "Obtains the integrated value accumulated into a Ray from an IntegralRayKernel-derived class.", "href": "../postprocessors/RayIntegralValue.html"}>>>
    ray_kernel<<<{"description": "The name of the IntegralRayKernel-derived RayKernel to obtain the integral value of"}>>> = aux_variable_integral
    ray<<<{"description": "Name of the Ray to get the final integral value from"}>>> = partial
  []
[]

(modules/ray_tracing/src/raykernels/VariableIntegralRayKernel.C)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#include "VariableIntegralRayKernel.h"

registerMooseObject("RayTracingApp", VariableIntegralRayKernel);

InputParameters
VariableIntegralRayKernel::validParams()
{
  InputParameters params = IntegralRayKernel::validParams();

  params.addClassDescription("Integrates a Variable or AuxVariable along a Ray.");

  params.addRequiredCoupledVar("variable", "The name of the variable to integrate");

  return params;
}

VariableIntegralRayKernel::VariableIntegralRayKernel(const InputParameters & params)
  : IntegralRayKernel(params), _u(coupledValue("variable"))
{
}

Real
VariableIntegralRayKernel::computeQpIntegral()
{
  return _u[_qp];
}

(modules/ray_tracing/test/tests/raykernels/variable_integral_ray_kernel/variable_integral_ray_kernel.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmax = 5
    ymax = 5
  []
[]

[Variables/u]
  [InitialCondition]
    type = FunctionIC
    variable = u
    function = '(x < 2) * (x + 2 * y) + (x >= 2) * (2 * x + 2 * y - 2)'
  []
[]

[AuxVariables/aux]
  order = CONSTANT
  family = MONOMIAL
  [InitialCondition]
    type = FunctionIC
    variable = u_ag
    function = 'x + y + cos(x)'
  []
[]


[UserObjects]
  [study]
    type = RepeatableRayStudy
    names = 'diag
             top_across
             bottom_across
             partial'
    start_points = '0 0 0
                    0 5 0
                    0 0 0
                    0.5 0.5 0'
    end_points = '5 5 0
                  5 5 0
                  5 0 0
                  4.5 0.5 0'
  []
[]

[RayKernels]
  [variable_integral]
    type = VariableIntegralRayKernel
    study = study
    variable = u
  []
  [aux_variable_integral]
    type = VariableIntegralRayKernel
    study = study
    variable = aux
  []
[]

[Postprocessors]
  [diag_value]
    type = RayIntegralValue
    ray_kernel = variable_integral
    ray = diag
  []
  [top_across_value]
    type = RayIntegralValue
    ray_kernel = variable_integral
    ray = top_across
  []
  [bottom_across_value]
    type = RayIntegralValue
    ray_kernel = variable_integral
    ray = bottom_across
  []
  [partial_value]
    type = RayIntegralValue
    ray_kernel = variable_integral
    ray = partial
  []

  [aux_diag_value]
    type = RayIntegralValue
    ray_kernel = aux_variable_integral
    ray = diag
  []
  [aux_top_across_value]
    type = RayIntegralValue
    ray_kernel = aux_variable_integral
    ray = top_across
  []
  [aux_bottom_across_value]
    type = RayIntegralValue
    ray_kernel = aux_variable_integral
    ray = bottom_across
  []
  [aux_partial_value]
    type = RayIntegralValue
    ray_kernel = aux_variable_integral
    ray = partial
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = false
  csv = true
[]

Description