Advection-Diffusion Equation with Absorbing Boundary

Grant, John and Wilkinson, Michael (2015). Advection-Diffusion Equation with Absorbing Boundary. Journal of Statistical Physics, 160(3) pp. 622–635.

DOI: https://doi.org/10.1007/s10955-015-1257-2

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: this method is more general than the method of images. 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.

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