AdamsPredictor

Implements an explicit Adams predictor based on two old solution vectors.

An Adams predictor is automatically added by MOOSE for the AB2PredictorCorrector time stepping/integration scheme.

The formula for the update by Adams' predictor is:

var element = document.getElementById("moose-equation-96b4cb2f-408d-40ed-9e52-f3fd31ad603b");katex.render("\\phi_{new} = A \\phi + B \\phi_{old} + C \\phi_{older}", element, {displayMode:true,throwOnError:false});

with \phi being the solution vector, including all degrees of freedom for the nonlinear variables and

var element = document.getElementById("moose-equation-dd18905c-bc8a-4450-9adc-66059b9002c7");katex.render("A = 1 + \\dfrac{\\Delta t}{\\Delta t_{old}} (1 + \\dfrac{\\Delta t}{2\\Delta t_{old}})", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-cc24711a-7e53-4e2f-bc23-361d61e87705");katex.render("B = - \\dfrac{\\Delta t}{\\Delta t_{old}} (1 + \\dfrac{\\Delta t}{2\\Delta t_{old}} + \\dfrac{\\Delta t}{2\\Delta t_{older}})", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-13cb1a7c-e2ad-4f38-af09-a7e0b164af1f");katex.render("C = \\dfrac{\\Delta t}{\\Delta t_{old}} \\dfrac{\\Delta t}{2\\Delta t_{older}}", element, {displayMode:true,throwOnError:false});

with $var element = document.getElementById("moose-equation-da5485c6-01f7-41da-b530-8e38c8ffe17d");katex.render("\\dfrac{\\Delta t}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-17f0b7bb-124a-46f3-b8d4-d2b60e40bb22");katex.render("\\dfrac{\\Delta t_{old}}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-db9782a6-033e-4849-a134-ec4269f889dd");katex.render("\\dfrac{\\Delta t_{older}}", element, {displayMode:false,throwOnError:false});$ being the current, previous and antepenultimate time steps sizes.

Example input syntax

In this example, an AdamsPredictor is implicitly being created by specifying the AB2PredictorCorrector time stepping scheme. The predictor is being used on every time step to perform a first update step.

[Executioner]
  type = Transient
  scheme = 'BDF2'
  #scheme = 'crank-nicolson'
  start_time = 0
  num_steps = 4
  nl_abs_tol = 1e-15
  petsc_options = '-snes_converged_reason'
  abort_on_solve_fail = true
  [./TimeStepper]
    type = AB2PredictorCorrector
    dt = .01
    e_max = 10
    e_tol = 1
  [../]
[]

Input Parameters

scaleThe scale factor for the predictor (can range from 0 to 1)
C++ Type:double
Controllable:No
Description:The scale factor for the predictor (can range from 0 to 1)

Required Parameters

order2The maximum reachable order of the Adams-Bashforth Predictor
Default:2
C++ Type:int
Controllable:No
Description:The maximum reachable order of the Adams-Bashforth Predictor
skip_after_failed_timestepFalseSkip prediction in a repeated time step after a failed time step
Default:False
C++ Type:bool
Controllable:No
Description:Skip prediction in a repeated time step after a failed time step
skip_timesSkip the predictor if the current solution time is in this list of times
C++ Type:std::vector<double>
Controllable:No
Description:Skip the predictor if the current solution time is in this list of times
skip_times_oldSkip the predictor if the previous solution time is in this list of times
C++ Type:std::vector<double>
Controllable:No
Description:Skip the predictor if the previous solution time is in this list of times

Optional 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:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

(moose/test/tests/time_integrators/aee/aee.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  nx = 10

  xmin = 0.0
  xmax = 1.0

[]

#still need BC for Energy, IC's for both.
[Variables]
  active = 'Time'

  [./Time]
    order =  FIRST
    family = LAGRANGE
    initial_condition = 0.0
  [../]
[]

[Functions]
  active = 'func'

  [./func]
    type = ParsedFunction
    expression = 2.0*t
  [../]
[]

[Kernels]
  active = 't_time func_time'

  [./t_time]
    type = TimeDerivative
    variable = Time
  [../]

  [./func_time]
    type = BodyForce
    variable = Time
    function = func
  [../]
[]

[BCs]
  active = 'Top_Temperature'

  [./Top_Temperature]
    type = NeumannBC
    variable = Time
    boundary = 'left right'
  [../]

[]

[Executioner]
  type = Transient
  scheme = 'BDF2'
  #scheme = 'crank-nicolson'
  start_time = 0
  num_steps = 4
  nl_abs_tol = 1e-15
  petsc_options = '-snes_converged_reason'
  abort_on_solve_fail = true
 [./TimeStepper]
    type = AB2PredictorCorrector
    dt = .01
    e_max = 10
    e_tol = 1
  [../]
[]

[Outputs]
  exodus = true
[]