NekVolumeNorm

Computes a finite L^N norm or an L-infinity norm of the difference between a NekRS solution field and an optional analytical function.

Description

This postprocessor computes either a finite integrated L $var element = document.getElementById("moose-equation-4080c3f4-c358-4ff7-8186-9d66a1bf4093");katex.render("^N", element, {displayMode:false,throwOnError:false});$ norm or the L $var element = document.getElementById("moose-equation-fa8e4923-a877-4f5a-a8ab-59035722e70e");katex.render("^\\infty", element, {displayMode:false,throwOnError:false});$ norm of a specified field over the NekRS mesh.

For finite $var element = document.getElementById("moose-equation-643e7640-9514-4a6a-9a1e-0b86d99b9ac4");katex.render("N \\geq 1", element, {displayMode:false,throwOnError:false});$ , the postprocessor evaluates

$var element = document.getElementById("moose-equation-447c8d41-09b2-41a6-b183-94792657a389");katex.render("p=\\left(\\int_{\\Omega}\\left|f-\\tilde{f}\\right|^N\\ d\\Omega\\right)^{1/N},", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-945d0576-eaba-4673-aa85-c4bad726c7ca");katex.render("p", element, {displayMode:false,throwOnError:false});$ is the value of the postprocessor, $var element = document.getElementById("moose-equation-d5b908bb-0fbc-4317-a7d3-88fd078fd0b5");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ is the volume of the NekRS mesh, $var element = document.getElementById("moose-equation-31f7d1f6-eb82-4301-a91f-848fa150ee39");katex.render("f", element, {displayMode:false,throwOnError:false});$ is the specified field, and $var element = document.getElementById("moose-equation-a122e839-ffb2-447b-a3ff-369bdbbd7b18");katex.render("\\tilde{f}", element, {displayMode:false,throwOnError:false});$ is an optional function provided by function.

When N = infinity, the postprocessor evaluates the nodal maximum norm

$var element = document.getElementById("moose-equation-f9941c14-dd54-472e-840d-a3a7346de9d2");katex.render("p=\\max_{\\boldsymbol{x}_i \\in \\Omega} \\left|f(\\boldsymbol{x}_i)-\\tilde{f}(\\boldsymbol{x}_i)\\right|,", element, {displayMode:true,throwOnError:false});$

The N parameter may be set to any real value greater than or equal to one, or to infinity.

To be clear, this postprocessor is not evaluated on the NekRSMesh mesh mirror, but instead on the mesh actually used for computation in NekRS.

The field is specified with the field parameter, which may be one of:

pressure: pressure
temperature: temperature
velocity: magnitude of velocity
velocity_x: $var element = document.getElementById("moose-equation-7b001d16-8f08-4701-944a-d5a2ec3d1cdc");katex.render("x", element, {displayMode:false,throwOnError:false});$ -component of velocity
velocity_y: $var element = document.getElementById("moose-equation-1303a319-acf9-43aa-b398-1547f062d4b4");katex.render("y", element, {displayMode:false,throwOnError:false});$ -component of velocity
velocity_z: $var element = document.getElementById("moose-equation-b619d70d-4268-44c7-82c3-fd88a8994889");katex.render("z", element, {displayMode:false,throwOnError:false});$ -component of velocity
velocity_x_squared: $var element = document.getElementById("moose-equation-421bfcfa-bfde-4c21-a12b-5aa732267b0e");katex.render("x", element, {displayMode:false,throwOnError:false});$ -component of velocity, squared
velocity_y_squared: $var element = document.getElementById("moose-equation-097ae8fa-46aa-4364-9dfa-86a6e56edc17");katex.render("y", element, {displayMode:false,throwOnError:false});$ -component of velocity, squared
velocity_z_squared: $var element = document.getElementById("moose-equation-f844640d-59fa-4a5e-abf9-a98578508c8e");katex.render("z", element, {displayMode:false,throwOnError:false});$ -component of velocity, squared
velocity_component: velocity vector dotted against another vector
scalar01: first non-temperature passive scalar
scalar02: second non-temperature passive scalar
scalar03: third non-temperature passive scalar
unity: the value 1.0
zero: the value 0.0 (this is typically used when combining with a function shift, to only apply the operation to the function)

Example Input Syntax

The following example evaluates the L $var element = document.getElementById("moose-equation-e5140411-2a30-4f70-8f8c-c495e4ddc770");katex.render("^2", element, {displayMode:false,throwOnError:false});$ , L $var element = document.getElementById("moose-equation-2857f376-e8fe-4bf1-8993-4ab65358e68c");katex.render("^1", element, {displayMode:false,throwOnError:false});$ , and L $var element = document.getElementById("moose-equation-83914a43-25f8-4cdc-afc1-9762053140e8");katex.render("^\\infty", element, {displayMode:false,throwOnError:false});$ norms of the NekRS temperature field relative to a function provided in the input file.

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [temp_l2]
    type = NekVolumeNorm<<<{"description": "Computes a finite L^N norm or an L-infinity norm of the difference between a NekRS solution field and an optional analytical function.", "href": "NekVolumeNorm.html"}>>>
    field<<<{"description": "Field to apply this object to"}>>> = temperature
    function<<<{"description": "Function to shift the field by, when applying this object. For example, if 'field = temperature', using this parameter will apply this object to the new combined quantity 'temperature - f', where 'f' is this shifting function."}>>> = function_to_compare
  []
  [temp_l2_comparison_b]
    type = NekVolumeIntegral<<<{"description": "Integral of a field over the NekRS volume mesh", "href": "NekVolumeIntegral.html"}>>>
    field<<<{"description": "Field to apply this object to"}>>> = velocity_x
  []
  [temp_l2_comparison]
    type = ParsedPostprocessor<<<{"description": "Computes a parsed expression with post-processors", "href": "ParsedPostprocessor.html"}>>>
    expression<<<{"description": "function expression"}>>> = 'sqrt(temp_l2_comparison_b)'
    pp_names<<<{"description": "Post-processors arguments"}>>> = 'temp_l2_comparison_b'
  []

  [temp_l1]
    type = NekVolumeNorm<<<{"description": "Computes a finite L^N norm or an L-infinity norm of the difference between a NekRS solution field and an optional analytical function.", "href": "NekVolumeNorm.html"}>>>
    field<<<{"description": "Field to apply this object to"}>>> = temperature
    N<<<{"description": "Order of the volume norm. Specify a finite real value N >= 1, or use 'infinity' for the L-infinity norm."}>>> = 1
    function<<<{"description": "Function to shift the field by, when applying this object. For example, if 'field = temperature', using this parameter will apply this object to the new combined quantity 'temperature - f', where 'f' is this shifting function."}>>> = function_to_compare
  []
  [temp_l1_comparison]
    type = NekVolumeIntegral<<<{"description": "Integral of a field over the NekRS volume mesh", "href": "NekVolumeIntegral.html"}>>>
    field<<<{"description": "Field to apply this object to"}>>> = velocity_y
  []

  [temp_linf]
    type = NekVolumeNorm<<<{"description": "Computes a finite L^N norm or an L-infinity norm of the difference between a NekRS solution field and an optional analytical function.", "href": "NekVolumeNorm.html"}>>>
    field<<<{"description": "Field to apply this object to"}>>> = temperature
    N<<<{"description": "Order of the volume norm. Specify a finite real value N >= 1, or use 'infinity' for the L-infinity norm."}>>> = infinity
    function<<<{"description": "Function to shift the field by, when applying this object. For example, if 'field = temperature', using this parameter will apply this object to the new combined quantity 'temperature - f', where 'f' is this shifting function."}>>> = function_to_compare
  []
  [temp_linf_comparison]
    type = NodalExtremeValue<<<{"description": "Finds either the min or max elemental value of a variable over the domain.", "href": "NodalExtremeValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = temperature_minus_function
  []

  [temp_without_function_linf]
    type = NekVolumeNorm<<<{"description": "Computes a finite L^N norm or an L-infinity norm of the difference between a NekRS solution field and an optional analytical function.", "href": "NekVolumeNorm.html"}>>>
    field<<<{"description": "Field to apply this object to"}>>> = temperature
    N<<<{"description": "Order of the volume norm. Specify a finite real value N >= 1, or use 'infinity' for the L-infinity norm."}>>> = infinity
  []
  [temp_without_function_linf_comparison]
    type = NodalExtremeValue<<<{"description": "Finds either the min or max elemental value of a variable over the domain.", "href": "NodalExtremeValue.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = temperature
  []
[]

(test/tests/postprocessors/nek_function_norm/nek.i)

[Problem]
  type = NekRSProblem
  casename = 'pyramid'
[]

[Mesh]
  type = NekRSMesh
  volume = true
[]

[Executioner]
  type = Transient

  [TimeStepper]
    type = NekTimeStepper
  []
[]

[AuxVariables]
  [temperature_minus_function]
  []
  [temperature]
  []
[]

[AuxKernels]
  [temperature_minus_function]
    type = FunctionAux
    variable = temperature_minus_function
    function = temperature_minus_function
  []
  [temperature]
    type = FunctionAux
    variable = temperature
    function = temperature
  []
[]

[Outputs]
  csv = true
  hide = 'temp_l2_comparison_b'
  execute_on = 'final'
[]

[Functions]
  [temperature]
    type = ParsedFunction
    expression = 'exp(x)+sin(y)+x*y*z'
  []
  [function_to_compare]
    type = ParsedFunction
    expression = 'exp(x*x)+0.7*y+0.8*z+1'
  []
  [temperature_minus_function]
    type = ParsedFunction
    expression = 'abs(temperature-function_to_compare)'
    symbol_names = 'temperature function_to_compare'
    symbol_values = 'temperature function_to_compare'
  []
[]

[Postprocessors]
  [temp_l2]
    type = NekVolumeNorm
    field = temperature
    function = function_to_compare
  []
  [temp_l2_comparison_b]
    type = NekVolumeIntegral
    field = velocity_x
  []
  [temp_l2_comparison]
    type = ParsedPostprocessor
    expression = 'sqrt(temp_l2_comparison_b)'
    pp_names = 'temp_l2_comparison_b'
  []

  [temp_l1]
    type = NekVolumeNorm
    field = temperature
    N = 1
    function = function_to_compare
  []
  [temp_l1_comparison]
    type = NekVolumeIntegral
    field = velocity_y
  []

  [temp_linf]
    type = NekVolumeNorm
    field = temperature
    N = infinity
    function = function_to_compare
  []
  [temp_linf_comparison]
    type = NodalExtremeValue
    variable = temperature_minus_function
  []

  [temp_without_function_linf]
    type = NekVolumeNorm
    field = temperature
    N = infinity
  []
  [temp_without_function_linf_comparison]
    type = NodalExtremeValue
    variable = temperature
  []
[]

Description
Example Input Syntax