  We explore the gap-tooth method for multiscale modeling of systems
represented by microscopic physics-based simulators, when coarse-grained
evolution equations are not available in closed form. A biased random walk
particle simulation, motivated by the viscous Burgers equation, serves as an
example. We construct macro-to-micro (lifting) and micro-to-macro (restriction)
operators, and drive the coarse time-evolution by particle simulations in
appropriately coupled microdomains (teeth) separated by large spatial gaps. A
macroscopically interpolative mechanism for communication between the teeth at
the particle level is introduced. The results demonstrate the feasibility of a
closure-on-demand approach to solving hydrodynamics problems.
