Advection diffusion equation with absorbing boundary

TL;DR

This paper derives asymptotic expressions for flux in a spatially homogeneous advection-diffusion system with general, time-independent parameters, focusing on large-distance behavior near steady sources and boundaries.

Contribution

It provides new asymptotic formulas for flux onto permeable and absorbing boundaries in a general advection-diffusion context.

Findings

Flux decays exponentially with distance from the source.

The decay exponent is identical for both permeable and absorbing boundaries.

Asymptotic expressions are valid at large distances from the source.

Abstract

We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point source, for the flux onto a completely permeable boundary and onto an absorbing boundary. The absorbing case is treated by making a source of antiparticles at the boundary. In both cases there is an exponential decay as the distance from the source increases; we find that the exponent is the same for both boundary conditions.