An optimal-transport finite-particle method for driven diffusion

We formulate a finite-particle method of mass transport that accounts for boundary conditions. The particle method couples a geometrically-exact treatment Wasserstein gradient-flow dynamics; and a Kullback-Leibler representation General boundary conditions are enforced by introducing an adsorption/depletion boundary wherein particles are added or removed as dictated by the boundary demonstrate the range and scope of the method through a number of examples including absorption of particles into a sphere and flow through pipes of square cross section, with and without occlusions. In all cases, the solution is observed weakly, or in the sense of local averages.