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External Variables Through v

The v variables represent externally supplied or auxiliary nodal fields that are not solved as the current PDE system's primary unknowns. In backend naming, these are odg; some frontend code also refers to this storage as vdg.

v is initialized by initv / Initv when generated, or supplied through mesh/input data when the application provides it.

Common Uses

  • Prescribed velocity or material fields.
  • Electromagnetic fields supplied by another model.
  • Atmospheric or database fields.
  • Reduced-order model predictions.
  • Coupled solver outputs.
  • Artificial-viscosity fields stored in mesh.vdg / odg.

Where v Can Enter

v can be used in:

  • Fluxes.
  • Sources.
  • EOS callbacks.
  • Auxiliary w equations.
  • Boundary conditions.
  • Initial conditions.
  • QoI and visualization callbacks.

Simple Pattern

For a scalar transport model with prescribed velocity \(a(x)\), store the velocity in v and write

\[ F(u,v) = v u. \]

This keeps the transported state u small while allowing the model to use a spatially varying prescribed field.

Do not confuse v with externalparam (uinf or eta). v is a nodal field; externalparam is a parameter vector.