Can I solve these coupled differential equations in MOOSE without creating a custom kernel?

[K-Komal-98]

I have solved a single second order differential equation using the ADMatdiffusion and Reaction kernel. Can you assist me on how to solve this problem with the existing moose kernels?

[GiudGiud]

Hello

The BCs are Dirichlet and Neumann, you can use off-the-shelf MOOSE BCs for this.

You ll want to write a new kernels (start from ADCoupledForce) for the u^2, v^2 and u^2 v^2 terms.

The second order space derivatives you can use a Diffusion kernel for the one that is in its own equation.
For the other one you ll need to create a coupledDiffusion kernel, that has a "variable" argument that is different than the variable that gets the second derivative taken from.

Guillaume

[K-Komal-98]

Can I use ADMatDiffusion kernel for the second order space derivatives. I have written a simple code for a problem attached here. Can you please guide me if this is a correct usage or not?

[Mesh]
    type = GeneratedMesh
    dim = 1
    nx = 60 
    xmax = 30
[]
[Variables]
    [u]
    []
    [v]
    []
[]

[Kernels]
  [1_diff_u]
    type = ADMatDiffusion
    diffusivity = 1
    variable = u
  []
  [1_diff_v]
    type = ADMatDiffusion
    diffusivity = 2
    variable = u
    v = v
  []
  [2_diff_u]
    type = ADMatDiffusion
    diffusivity = 3
    variable = v
    v = u
  []
  [2_diff_v]
    type = ADMatDiffusion
    diffusivity = 4
    variable = v
  []
[]

[BCs]
  [left_u]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right_u]
    type = DirichletBC
    variable = u
    boundary = right
    value = 10
  []
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 10
  []
[]
[Executioner]
     type = Steady
     nl_max_its = 100
     solve_type = Newton
[]
[VectorPostprocessors]
  [u]
    type = NodalValueSampler
    sort_by = id
    variable = u
  []
  [v]
    type = NodalValueSampler
    sort_by = id
    variable = v
  []
[]
[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

[GiudGiud]

Yes this seems fine actually

[K-Komal-98]

Thank you