automated convergence testing using MMS

[BenWibking]

Describe the proposal
Use the Method of Manufactured Solutions (Roache 2001) to produce test problems that are nonlinear (but smooth!) for the radiation hydro equations, then add them to the test suite and verify that our code produces the expected (2nd) order of convergence.

Describe alternatives you've considered
Use existing test problems, and don't verify the order of convergence as part of the test suite.

Additional context

• Generic example: https://mooseframework.inl.gov/python/mms.html
• Radiation diffusion: https://www.osti.gov/biblio/1264215
• Radiation moment equations (see section 7.1): https://www.sciencedirect.com/science/article/pii/S0021999122008105#se0190
• Radiation hydro equations: https://www.osti.gov/biblio/1724326
  • "A second verification of the multirate time integration is the Taylor-Green-Brunner radiation hydrodynamics problem. This
    problem is run in pure Lagrange mode with a prescribed velocity according to the equations for a Taylor-Green vortex. The
    radiation source is such that it should exactly cancel the hydrodynamic pressure, the resulting density should remain constant."