  The partial differential equations describing compressible fluid flows can be
notoriously difficult to resolve on a pragmatic scale and often require the use
of high performance computing systems and/or accelerators. However, these
systems face scaling issues such as latency, the fixed cost of communicating
information between devices in the system. The swept rule is a technique
designed to minimize these costs by obtaining a solution to unsteady equations
at as many possible spatial locations and times prior to communicating. In this
study, we implemented and tested the swept rule for solving two-dimensional
problems on heterogeneous computing systems across two distinct systems. Our
solver showed a speedup range of 0.22-2.71 for the heat diffusion equation and
0.52-1.46 for the compressible Euler equations. We can conclude from this study
that the swept rule offers both potential for speedups and slowdowns and that
care should be taken when designing such a solver to maximize benefits. These
results can help make decisions to maximize these benefits and inform designs.
