High Performance Computing (HPC) is a key enabling tool to interconnect the many, varied simulation capabilities required to advance the science of groundwater remediation. The US Army Engineer Waterways Experiment Station is engaged in research and development that will provide a seamless link to tools that combine diverse field data into accurate site characterizations, and perform computer simulations of remediation processes. However, the simulation models on which this capability is founded are still not adequate to simulate real, heterogeneous media that make up the natural groundwater environment. The inadequacy stems from the multi-scale structure of natural media that is masked by the continuum formulations upon which numerical models are based. The range of scales is simply too great to be spanned by any present, or foreseeable, HPC resource. To advance the science of multi-scale simulation, HPC may be viewed as an extension of the laboratory. By stretching present resources to perform scale-spanning simulations, stochastic models are created from data that could not be obtained previously from physical experiments. A detailed description of this process is presented for non-reactive, dispersive transport.