Advection-Diffusion Equation with Absorbing Boundary
Grant, John, Michael Wilkinson · Open Research Online - ORO (The Open University) · 2015
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.