EqualValueEmbeddedConstraint

This is a constraint enforcing overlapping portions of two blocks to have the same variable value

This is a constraint acting upon overlapping portions of two blocks, a secondary block and a primary block. The constraint enforces the secondary variable on the secondary block and the primary variable on the primary block to have the same values. The mesh dimensions of the two blocks do not have to match.

The constraint iterates through all the nodes on the secondary block and searches for a primary element that contains each secondary node. If a secondary node is located within an element, then a constraint is applied to force the secondary node to have the same value as the solution variable in the primary element, evaluated at the location of the secondary point.

This can be used for a number of applications. For example, in mechanics problems, it can be used to connect lower dimensional elements such as 1D truss elements to 2D or 3D continuum elements. This can be used to model reinforcement in a way that does not require the reinforcement and continuum meshes to have coincident nodes.

Mathematical Formulation

Options are available to control how this constraint is applied:

Kinematic

This option strictly enforces value of the solution at the secondary nodes to be equal to the value in the primary element at that point. The constraint is enforced by updating the secondary residual $var element = document.getElementById("moose-equation-4d2afc0a-c5ed-45c7-8ff3-c2fd7cfe7e89");katex.render("r_s", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and primary residual $var element = document.getElementById("moose-equation-9ece536b-7774-4ff4-87f5-d9cc2e381c17");katex.render("r_m", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ as: $var element = document.getElementById("moose-equation-2796ca77-9b69-4f11-bf89-b11705a1e257");katex.render("\\begin{aligned} r_s &= r_s + f_c + k_p(u_{secondary} - u_{primary})\\\\ r_m &= r_m + \\phi_i r_{s,copy} \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-534a3fe5-08e8-4e85-9881-27f1ebddc567");katex.render("r_{s,copy}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a copy of the residual of the secondary node before the constraint is applied and $var element = document.getElementById("moose-equation-b5474049-7059-4528-8336-98da7f04ea8d");katex.render("k_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the user-specified penalty parameter. This formulation uses the penalty parameter only to penalize the error, and the converged solution has no error due the penalty. The penalty factor must be specified, and should be consistent with the scaling for the solution variable to which this is applied.

Penalty

This option uses a penalty formulation in which the error in the solution is proportional to a user-specified penalty parameter $var element = document.getElementById("moose-equation-937764d8-9797-4b82-bc25-f22927801dc3");katex.render("k_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . The constraint is enforced by modifying the secondary and primary residual The constraint is enforced by updating the secondary residual $var element = document.getElementById("moose-equation-5152ac34-e7dd-4651-b882-65c4785847fe");katex.render("r_s", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and primary residual $var element = document.getElementById("moose-equation-8865c0bf-58bc-483f-9b23-60916d3e6249");katex.render("r_m", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ as: $var element = document.getElementById("moose-equation-a00828ba-8c3a-4844-888e-23e77eaa9547");katex.render("\\begin{aligned} r_s &= r_s + k_p(u_{secondary} - u_{primary})\\\\ r_m &= r_m - \\phi_i k_p(u_{secondary} - u_{primary}) \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-82cb5325-4f34-4ab2-847e-eefc8d1c9152");katex.render("r_{s,copy}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the ghosted residual. The penalty parameter must be selected carefully, as small values lead to large differences between the secondary node's solution and the solution in the primary element, while large values may lead to poor convergence.

Input Parameters

penaltyPenalty parameter used in constraint enforcement for kinematic and penalty formulations.
C++ Type:double
Controllable:No
Description:Penalty parameter used in constraint enforcement for kinematic and penalty formulations.
primaryprimary block id
C++ Type:SubdomainName
Controllable:No
Description:primary block id
primary_variableThe variable on the primary side of the domain
C++ Type:std::vector<VariableName>
Controllable:No
Description:The variable on the primary side of the domain
secondarysecondary block id
C++ Type:SubdomainName
Controllable:No
Description:secondary block id
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

formulationkinematicFormulation used to enforce the constraint
Default:kinematic
C++ Type:MooseEnum
Options:kinematic, penalty
Controllable:No
Description:Formulation used to enforce the constraint

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

Input Files

(modules/heat_transfer/test/tests/truss_heat_conduction/block_w_line.i)
(modules/heat_transfer/test/tests/truss_heat_conduction/rectangle_w_line.i)
(test/tests/constraints/equal_value_embedded_constraint/embedded_constraint.i)

(modules/heat_transfer/test/tests/truss_heat_conduction/block_w_line.i)

[Mesh]
  parallel_type = 'replicated'
  [block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 50
    nz = 1
    xmin = -0.5
    xmax = 0.5
    ymin = -1.25
    ymax = 1.25
    zmin = -0.04
    zmax = 0.04
    boundary_name_prefix = block
  []
  [block_id]
    type = SubdomainIDGenerator
    input = block
    subdomain_id = 1
  []
  [line]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = -0.5
    xmax = 0.5
    nx = 10
    boundary_name_prefix = line
    boundary_id_offset = 10
  []
  [line_id]
    type = SubdomainIDGenerator
    input = line
    subdomain_id = 2
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'block_id line_id'
  []
  [line_rename]
    type = RenameBlockGenerator
    input = combined
    old_block = '1 2'
    new_block = 'block line'
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
    block = 'block'
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 'block'
  []
  [time_derivative_line]
    type = TrussHeatConductionTimeDerivative
    variable = temperature
    area = area
    block = 'line'
  []
  [heat_conduction_line]
    type = TrussHeatConduction
    variable = temperature
    area = area
    block = 'line'
  []
[]

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

[AuxKernels]
  [area]
    type = ConstantAux
    variable = area
    value = 0.008
    execute_on = 'initial timestep_begin'
  []
[]

[Constraints]
  [equalvalue]
    type = EqualValueEmbeddedConstraint
    secondary = 'line'
    primary = 'block'
    penalty = 1e6
    formulation = kinematic
    primary_variable = temperature
    variable = temperature
  []
[]

[Materials]
  [block]
    type = GenericConstantMaterial
    block = 'block'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [line]
    type = GenericConstantMaterial
    block = 'line'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '10.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'block_right line_right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [x_n0_25]
    type = LineValueSampler
    start_point = '-0.25 0 0'
    end_point = '-0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
  [x_0_25]
    type = LineValueSampler
    start_point = '0.25 0 0'
    end_point = '0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/block_w_line'
    time_data = true
  []
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/rectangle_w_line.i)

[Mesh]
  parallel_type = 'replicated'
  [rectangle]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 50
    xmin = -0.5
    xmax = 0.5
    ymin = -1.25
    ymax = 1.25
    boundary_name_prefix = rectangle
  []
  [rectangle_id]
    type = SubdomainIDGenerator
    input = rectangle
    subdomain_id = 1
  []
  [line]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = -0.5
    xmax = 0.5
    nx = 10
    boundary_name_prefix = line
    boundary_id_offset = 10
  []
  [line_id]
    type = SubdomainIDGenerator
    input = line
    subdomain_id = 2
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'rectangle_id line_id'
  []
  [blcok_rename]
    type = RenameBlockGenerator
    input = combined
    old_block = '1 2'
    new_block = 'rectangle line'
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
    block = 'rectangle'
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 'rectangle'
  []
  [time_derivative_line]
    type = TrussHeatConductionTimeDerivative
    variable = temperature
    area = area
    block = 'line'
  []
  [heat_conduction_line]
    type = TrussHeatConduction
    variable = temperature
    area = area
    block = 'line'
  []
[]

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

[AuxKernels]
  [area]
    type = ConstantAux
    variable = area
    value = 0.1 # strip thickness
    execute_on = 'initial timestep_begin'
  []
[]

[Constraints]
  [equalvalue]
    type = EqualValueEmbeddedConstraint
    secondary = 'line'
    primary = 'rectangle'
    penalty = 1e6
    formulation = kinematic
    primary_variable = temperature
    variable = temperature
  []
[]

[Materials]
  [rectangle]
    type = GenericConstantMaterial
    block = 'rectangle'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [line]
    type = GenericConstantMaterial
    block = 'line'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '10.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'rectangle_right line_right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [x_n0_25]
    type = LineValueSampler
    start_point = '-0.25 0 0'
    end_point = '-0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
  [x_0_25]
    type = LineValueSampler
    start_point = '0.25 0 0'
    end_point = '0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/rectangle_w_line'
    time_data = true
  []
[]

(test/tests/constraints/equal_value_embedded_constraint/embedded_constraint.i)

###########################################################
# This is a test that demonstrates a user-defined
# constraint. It forces variables in overlapping portion of
# two blocks to have the same value
###########################################################

[Mesh]
[]

[Variables]
  [phi]
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [diffusion]
    type = Diffusion
    variable = phi
  []
[]

[BCs]
  [top]
    type = DirichletBC
    variable = phi
    boundary = 1
    value = 10.0
  []
  [bottom]
    type = DirichletBC
    variable = phi
    boundary = 2
    value = 0.0
  []
  [left]
    type = DirichletBC
    variable = phi
    boundary = 3
    value = 10.0
  []
  [right]
    type = DirichletBC
    variable = phi
    boundary = 4
    value = 0.0
  []
[]

[Constraints]
  [equal]
    type = EqualValueEmbeddedConstraint
    secondary = 2
    primary = 1
    penalty = 1e3
    primary_variable = phi
    variable = phi
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = none
  nl_rel_tol = 1e-15
  nl_abs_tol = 1e-8
  l_max_its = 100
  nl_max_its = 10
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

Mathematical Formulation
Input Parameters
Input Files