VolumetricHeatSource

Description

Sets an initial condition while preserving a total specified volume integral. The VolumetricHeatSource is not an actual object in Cardinal, but only a convenience wrapper around the IntegralPreservingFunctionIC in MOOSE, which defines an initial condition as the combination of a function and a total "magnitude" (integral) that should be preserved. This action applies the initial condition:

$(1)var element = document.getElementById("moose-equation-28038a32-40c7-4d36-aff8-daf80547a1b2");katex.render(" u(\\vec{r}, t_0) = q_0 f(\\vec{r}, t_0)", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-c7cf488c-4173-418c-a08e-a493e8a0e915");katex.render("u", element, {displayMode:false,throwOnError:false});$ is the variable, $var element = document.getElementById("moose-equation-a29d46ad-cc1a-4be1-9148-f5fb60656b81");katex.render("f", element, {displayMode:false,throwOnError:false});$ is the function, and $var element = document.getElementById("moose-equation-4d81003f-f7d2-4e64-a710-74b5400f0aa7");katex.render("q_0", element, {displayMode:false,throwOnError:false});$ is a scaling factor used to preserve a total magnitude upon volume integration:

$(2)var element = document.getElementById("moose-equation-b2d00af6-8afd-4760-9099-00fd31811dd7");katex.render(" q_0=\\frac{Q}{\\int_\\Omega fd\\Omega}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-40ab20fd-8f70-4faf-9e91-0759a83c1289");katex.render("Q", element, {displayMode:false,throwOnError:false});$ is the total magnitude and $var element = document.getElementById("moose-equation-b40a390a-14fc-47fb-84aa-873fb6189743");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ is the domain of integration. The parameters that must be provided for this action are:

variable: Variable to apply the initial condition to
function: Function providing the shape of the heat source
magnitude: Desired integrated total magnitude of the heat source

Example Input Syntax

We use custom Cardinal syntax in order to simplify setup of this initial condition. As an example, below we set a sinusoidal heat source with generic form $var element = document.getElementById("moose-equation-b6ac5734-550b-4024-bfce-c098adb6c73a");katex.render("\\sin{\\left(\\frac{\\pi z}{H}\\right)}", element, {displayMode:false,throwOnError:false});$ for a total magnitude of 550 (upon volume integration). This means that the actual initial condition is $var element = document.getElementById("moose-equation-ed17bf08-e304-4ab4-9b69-1d4e769978c5");katex.render("q_0\\sin{\\left(\\frac{\\pi z}{H}\\right)}", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-d6c569b6-4bc6-4446-99f1-06db0b32a60a");katex.render("q_0", element, {displayMode:false,throwOnError:false});$ is determined in order to satisfy the specified total volume integral.

[Cardinal]
  [ICs]
    [VolumetricHeatSource]
      variable = power
      magnitude = 550.0
      function = 'sin(pi * z / 1.9)'
    []
  []
[]

(test/tests/ics/volumetric_heat_source_ic/sinusoidal_z.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 5
  ny = 5
  nz = 20
  xmax = 1.5
  ymax = 1.7
  zmax = 1.9
  xmin = 0.0
  ymin = 0.0
  zmin = 0.0
[]

[Problem]
  type = FEProblem
  solve = false
[]

[AuxVariables]
  [power]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Cardinal]
  [ICs]
    [VolumetricHeatSource]
      variable = power
      magnitude = 550.0
      function = 'sin(pi * z / 1.9)'
    []
  []
[]

[Postprocessors]
  [integrated_power] # should equal 550
    type = ElementIntegralVariablePostprocessor
    variable = power
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax