Boundary conditions

Users may impose no-penetration, flux, gradient (Neumann), and value (Dirichlet) boundary conditions in bounded, non-periodic directions. Note that the only boundary condition available for a velocity field normal to the bounded direction is no-penetration.

Flux boundary conditions

A flux boundary condition prescribes flux of a quantity normal to the boundary. For a tracer this corresponds to prescribing

where is an external boundary.

Gradient (Neumann) boundary condition

A gradient boundary condition prescribes the gradient of a field normal to the boundary. For a tracer this prescribes

Value (Dirichlet) boundary condition

A value boundary condition prescribes the value of a field on a boundary; for a tracer this prescribes

No penetration boundary condition

A no penetration boundary condition prescribes the velocity component normal to a boundary to be 0, so that