Boundary conditions for stochastic solutions of the convection-diffusion equation

Stochastic methods offer an attractively simple solution to complex transport-controlled problems, and have a wide range of physical, chemical, and biological applications. Stochastic methods do not suffer from the numerical diffusion that plagues grid-based methods, but they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce some ideas and algorithms that can be used to implement boundary conditions in stochastic simulations of the convection-diffusion equation with accuracies comparable to the bulk phase. The algorithms have been tested in two-dimensional channel flows over a range of Peclet numbers, and compared with independent finite-difference calculations.