Step 3: Add Phase Decomposition to the Model

Initial Conditions

We know that the initial conditions should be 46.774 mol% chromium with minor variations. We will input this using random initial conditions.

[ICs]
  [concentrationIC]   # 46.774 mol% Cr with variations
    type = RandomIC
    min = 0.44774
    max = 0.48774
    seed = 210
    variable = c
  []
[]

Note that the seed is the random number generator seed. It should not effect how the simulation behaves.

Solution Time

Before we were just running the simulation long enough to begin to see the behavior. Now we want to run it for the full seven days. We change this in the executioner block.

end_time = 604800   # 7 days

Mesh Adaptivity

In order to accurately calculate the phase interfaces, we need a relatively fine mesh. However, in the bulk of the phases we can significantly speed up the solution by using a coarse mesh. Luckily, MOOSE comes equipped to let us refine the mesh where we need extra accuracy and coarsen it where we don't. We change the mesh block to look like this:

[Mesh]
  type = GeneratedMesh
  dim = 2
  distribution = DEFAULT
  elem_type = QUAD4
  nx = 25
  ny = 25
  nz = 0
  xmin = 0
  xmax = 25
  ymin = 0
  ymax = 25
  zmin = 0
  zmax = 0
  uniform_refine = 2
[]

The basic mesh is 25 × 25 elements. This defines the coarsest the mesh can be. The uniform_refine option refines the mesh for the first time step to be a 100 × 100 element mesh. If we do not turn on mesh adaptivity, the mesh would remain 100 × 100 throughout the simulation and it would be the exact same mesh we have used already.

To add mesh adaptivity, we go back to the executioner block, add the adaptivity sub-block, and tell it we want the maximum refinement level to be two factors finer than the coarsest mesh allowed.

[Executioner]
  type = Transient
  solve_type = NEWTON
  l_max_its = 30
  l_tol = 1e-6
  nl_max_its = 50
  nl_abs_tol = 1e-9
  end_time = 604800   # 7 days
  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type
                         -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  preonly
                         ilu          1'
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 10
    cutback_factor = 0.8
    growth_factor = 1.5
    optimal_iterations = 7
  []
  [Adaptivity]
    coarsen_fraction = 0.1
    refine_fraction = 0.7
    max_h_level = 2
  []
[]

Postprocessors

With the mesh adaptivity turned on, we are now interested in how many elements the surface has. We can calculate this by turning the NumNodes Postprocessor on.

We are also interested in how the size of the time step changes throughout the simulation, so we add a TimeStepSize Postprocessor. We can also look at the number of iterations at each time step.

[Postprocessors]
  [step_size]             # Size of the time step
    type = TimestepSize
  []
  [iterations]            # Number of iterations needed to converge timestep
    type = NumNonlinearIterations
  []
  [nodes]                 # Number of nodes in mesh
    type = NumNodes
  []
  [evaluations]           # Cumulative residual calculations for simulation
    type = NumResidualEvaluations
  []
  [active_time]           # Time computer spent on simulation
    type = PerformanceData
    event =  ACTIVE
  []
[]