• The first step is to solve a simple "Diffusion" problem, which requires no code:

$$$$-\nabla\cdot\nabla p = 0$$$$

  • Which will have a weak form of:

$$$$\left (\nabla p, \nabla \psi_i \right ) - \left < \nabla p \cdot \mathbf{n}, \psi_i \right > = 0$$$$

  • For now, ignore the boundary term (set $$$\nabla p \cdot \mathbf{n} = 0$$$ )
  • This is similar to the pressure equation we need for Darcy flow
  • Use the Diffusion object that already exists in MOOSE (no code necessary!)
  • Need to specify the geometry and set up an axisymmetric problem
  • Further, define boundary conditions to impose the pressure in each tank
  • All of this can be accomplished in the input file...

Diffusion Input File

step1.i

Create a Test

  • Create a simple test that mimics the behavior of the problem above, but use a smaller mesh to increase the speed.

tutorials/darcy_thermo_mech/step1_diffusion/tests/bcs/diffusion/tests

tutorials/darcy_thermo_mech/step1_diffusion/tests/bcs/diffusion/diffusion.i