Numerical Implementation of Streaming Down the Gradient: Application to Fluid Modeling of Cosmic Rays and Saturated Conduction

Understand

The equation governing the streaming of a quantity down its gradient superficially looks similar to the simple constant velocity advection equation.

• In fact, it is the same as an advection equation if there are no local extrema in the computational domain or at the boundary.
• However, in general when there are local extrema in the computational domain it is a non-trivial nonlinear equation.
• The standard upwind time evolution with a CFL-limited time step results in spurious oscillations at the grid scale.