DIVERGED_BREAKDOWN in a coupled Allen-Cahn , Cahn-Hillard problem

[mehdikamyabi]

Dear MOOSE developers and experts,
I hope you are well.
recently I tried to solve Allen-Cahn model, coupled with Cahn-Hillard to see the Ostwald ripening phenomena. this is the input file:

=========================================================

OSTWALD RIPENING + ALLEN-CAHN GRAINS

Allen–Cahn (eta_i) + Monolithic Cahn–Hilliard (c)

=========================================================

=========================================================

SINTERING + OSTWALD RIPENING (NO TEMPERATURE)

Allen–Cahn (eta_i) + Cahn–Hilliard (c)

=========================================================

[Mesh]
type = GeneratedMesh
dim = 2
nx = 100
ny = 100
xmin = 0
xmax = 100
ymin = 0
ymax = 100
[]

=========================================================

VARIABLES

=========================================================

[Variables]

conserved field (diffusing material / density)

[c]
order = FIRST
family = LAGRANGE
initial_condition = 0.2
[]

order parameters (particles)

[eta0]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = SpecifiedSmoothCircleIC
invalue = 1.0
outvalue = 0.0
radii = 12
x_positions = 35
y_positions = 35
z_positions = '0'
int_width = 5
[]
[]

[eta1]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = SpecifiedSmoothCircleIC
invalue = 1.0
outvalue = 0.0
radii = 10
x_positions = 65
y_positions = 35
z_positions = '0'
int_width = 5
[]
[]

[eta2]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = SpecifiedSmoothCircleIC
invalue = 1.0
outvalue = 0.0
radii = 8
x_positions = 35
y_positions = 65
z_positions = '0'
int_width = 5
[]
[]

[eta3]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = SpecifiedSmoothCircleIC
invalue = 1.0
outvalue = 0.0
radii = 6
x_positions = 65
y_positions = 65
z_positions = '0'
int_width = 5
[]
[]

[w]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]

[]

=========================================================

ICs

#[ICs]

[c_ic]

type = RandomIC

variable = c

#min = 0.199
#max = 0.201

#[]
#[]

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KERNELS

=========================================================

[Kernels]

=========================================================

Allen–Cahn (reaction terms for eta fields)

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[eta0_ac]
type = AllenCahn
variable = eta0
f_name = f_total
mob_name = L
coupled_variables = 'eta0 eta1 eta2 eta3 c'
[]

[eta1_ac]
type = AllenCahn
variable = eta1
f_name = f_total
mob_name = L
coupled_variables = 'eta0 eta1 eta2 eta3 c'
[]

[eta2_ac]
type = AllenCahn
variable = eta2
f_name = f_total
mob_name = L
coupled_variables = 'eta0 eta1 eta2 eta3 c'
[]

[eta3_ac]
type = AllenCahn
variable = eta3
f_name = f_total
mob_name = L
coupled_variables = 'eta0 eta1 eta2 eta3 c'
[]

=========================================================

IMPORTANT: gradient energy for eta (interface physics)

=========================================================

[eta0_grad]
type = ACInterface
variable = eta0
kappa_name = kappa_eta
[]

[eta1_grad]
type = ACInterface
variable = eta1
kappa_name = kappa_eta
[]

[eta2_grad]
type = ACInterface
variable = eta2
kappa_name = kappa_eta
[]

[eta3_grad]
type = ACInterface
variable = eta3
kappa_name = kappa_eta
[]

=========================================================

Cahn–Hilliard system for c

=========================================================

[c_dot]
type = TimeDerivative
variable = c
[]

#[c_ch]

type = CahnHilliard

variable = c

f_name = f_total

#mobility_name = M
#kappa_name = kappa_c

#[]

[c_flux]
type = SplitCHWRes
variable = c
mob_name = M
w = w
[]

[w_def]
type = SplitCHParsed
variable = w
f_name = f_total
kappa_name = kappa_c
w = c
coupled_variables = 'eta0 eta1 eta2 eta3 c'
[]

[]# =========================================================

MATERIALS

=========================================================

[Materials]

free energy (Allen–Cahn + Ostwald coupling)

[free_energy]
type = DerivativeParsedMaterial
property_name = f_total
expression = "W/4*((eta0^2-1)^2+(eta1^2-1)^2+(eta2^2-1)^2+(eta3^2-1)^2)+gamma*(eta0^2eta1^2+eta0^2eta2^2+eta0^2eta3^2+eta1^2eta2^2+eta1^2eta3^2+eta2^2eta3^2)+A*(c^2*(1-c)^2) +lamc(eta0^2+eta1^2+eta2^2+eta3^2)"
coupled_variables = 'eta0 eta1 eta2 eta3 c'
constant_names = 'W gamma A lam'
constant_expressions = '1 1 0.2 0'
derivative_order = 2
[]

mobilities

[mob_eta]
type = GenericConstantMaterial
prop_names = 'L'
prop_values = '1'
[]

[mob_c]
type = GenericConstantMaterial
prop_names = 'M'
prop_values = '0.05'
[]

gradient energy for CH

[kappa_c]
type = GenericConstantMaterial
prop_names = 'kappa_c'
prop_values = '0.5'
[]
[kappa_eta]
type = GenericConstantMaterial
prop_names = 'kappa_eta'
prop_values = '5.0'
[]

[]

=========================================================

BOUNDARY CONDITIONS (NO FLUX)

=========================================================

[BCs]

[c_noflux]
type = NeumannBC
variable = c
boundary = 'left right top bottom'
value = 0
[]

[]

=========================================================

EXECUTIONER

=========================================================

[Executioner]
type = Transient
scheme = bdf2
dt = 1e-7 # Not too small, not too large
end_time = 1.0

solve_type = PJFNK

petsc_options_iname = '-pc_type -ksp_type -sub_pc_type -pc_asm_overlap'
petsc_options_value = 'asm gmres lu 2'

nl_rel_tol = 1e-4
nl_abs_tol = 1e-6
nl_max_its = 20

l_tol = 1e-2
l_max_its = 300

line_search = 'bt'
[]# =========================================================

==================== OUTPUTS ====================

[Outputs]

خروجی odus برای پاراویو

exodus = true
csv = true
time_step_interval = 1000
execute_on = 'initial timestep_end'

کنسول

[console]
type = Console
output_linear = false
output_nonlinear = true
perf_log = true
execute_on = 'timestep_end'
[]

checkpoint برای restart

[checkpoint]

type = Checkpoint

num_files = 2

interval = 1000

#[]

[]

=========================================================

DEBUG

=========================================================

[Debug]
show_var_residual_norms = true
[]

but I faced with divergence exactly at the start of the iterations:

Time Step 0, time = 0

Time Step 1, time = 1e-07, dt = 1e-07
Linear solve did not converge due to DIVERGED_BREAKDOWN iterations 30

I tired too much to fix it by using Cahn-Hillard kernel instead of SplitCHWRes+ SplitCHParsed, by using a randomized noisy initial condition for concentration, by reducing time step and by forced decoupling (lam=0) but the error didn't eliminate.
may you please help me with this?

[GiudGiud]

Hello

Have you tried the suggestions in the troubleshooting failed solves help page on the moose website?

There is additional info there we can use to troubleshoot

[mehdikamyabi]

Hello,
do you mean this page?:
https://mooseframework.inl.gov/help/troubleshooting.html

it doesn't discuss about the error I faced. maybe you mean something else?

[GiudGiud]

no actually this one
https://mooseframework.inl.gov/application_usage/failed_solves.html