- 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...

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# Diffusion Input File

[step1.i](https://github.com/idaholab/moose/blob/devel/tutorials/darcy_thermo_mech/step01_diffusion/problems/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](https://github.com/idaholab/moose/blob/devel/tutorials/darcy_thermo_mech/step01_diffusion/tests/bcs/diffusion/tests)

[](---)

[tutorials/darcy_thermo_mech/step1_diffusion/tests/bcs/diffusion/diffusion.i](https://github.com/idaholab/moose/blob/devel/tutorials/darcy_thermo_mech/step01_diffusion/tests/bcs/diffusion/diffusion.i)