time

Definitions of the temporal discretizations for the scalar transport equation.

At the continuous level, we solve the current PDE:

\[\partial_t u + f(u) + g(u, \nabla u) = 0,\]

where \(f(u) = \nabla \cdot (\bm{b} u)\) is the inviscid flux and \(g(u, \nabla u) = \nabla \cdot (\kappa \nabla u)\) is the viscous flux.

note:

The spatial fluxes are discretized, assuming they are on the left-hand side, see above.

explicit	Definitions of explicit time marching schemes for a scalar transport equation.
imex	Definitions of the implicit-explicit (IMEX) time schemes for the scalar transport equation.
implicit	Definitions of implicit time marching schemes for a scalar transport equation.