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Modeling wave propagation through the earth is an important application in geoscience. We present a framework for wave propagation modeling on special-purpose hardware, which dramatically improves the application performance compared to conventional CPUs. We utilize custom hardware platforms consisting of a mix of x86 CPUs and dataflow engines connected by high-bandwidth communication links. Application programmers describe their algorithms in a domain specific language using Java syntax, with special dataflow semantics overlayed on top of the Java language. The application-specific dataflow engines run at hundreds of MHz with massive parallelism and deliver high performance/Watt, up to 30 times more energy efficient than conventional CPUs. The power efficiency of this approach suggests that dataflow computing may have a key role to play in the improvements in power efficiency necessary to reach exascale computing.