Burgers Equation (Convection - Diffusion 1D)

[emvalbuena]

Goal: show the reduction works with an easy-to-interpret non-linear operator.

• FOM Solver:
  • Integration scheme.
  • Stabilisation terms.
  • ENH : Mass conservation #55
  • ENH : Compute the force exerted by the flow on the piston #56
• ROM Solver:
  • Hyper-reduction of a solution-dependent non-linearity.

Suggestions from Steven:

• Piston with a moving domain.
• Interacting waves (here the non-linearity is a bit more complex to "feel")

FeniCs:

• https://github.com/SourangshuGhosh/burgers_time_viscous/blob/master/burgers_time_viscous.py

[emvalbuena]

Looking good for the moment.

I need to go back to the ALE terms and make sure I am implementing them in the right way.
Also, it would be nice to compute the density and the speed of sound, so that I can correctly compute the Mach number and the conservation of mass.