A fully-developed boundary condition for the random walk particle tracking method

Abstract

Random walk particle tracking (RWPT) is an effective and flexible approach to resolve scalar transport in direct numerical simulations (DNS) of single and multi-phase flows. It is often part of a hybrid scheme where the flow field is recovered by a separate hydrodynamic solver and the scalar field is resolved by RWPT. Since RWPT method tracks the displacement of passive Brownian tracers, rather than discretizing the advection–diffusion equation, development of boundary conditions for RWPT is not trivial. Namely, rules imposed upon a single tracer at the boundary must, after averaging, recover the desired continuum scale boundary condition. Here we develop means for imposing a fully-developed outflow boundary condition for the RWPT method. The technique developed here utilizes a semi-reflecting barrier at the outflow boundary. Tracers that reach the boundary plane are either reflected back into the domain or allowed to vacate the domain. We show that the semi-reflecting barrier developed here converges to the classic reflective boundary and open boundary in the asymptotic limit of low and high Peclet number, respectively. The new outflow boundary condition is verified against boundary layer (BL) theory for flow past a hot plate. The temperature field extracted at the outflow boundary is observed to be in agreement with BL solutions.