This project concerns the dynamical transport of heat and matter in Earths mantle and core. Mantle convection shapes the surface by building mountains, dispersing and aggregating continents, and guiding the structure and evolution of the environment at Earths surface; on short time scales, it causes earthquakes and volcanic eruptions. Through thermal transport it also affects patterns of heat flux out of the core, which in turn influences convection in Earths fluid outer core. Convection of core fluid maintains the geomagnetic field, which, at the surface, affects navigation and communication and helps to shield Earth from cosmic radiation. We undertake computer-intensive studies of the 3-dimensional dynamics of the mantle and core through both simulations and analyses of observational data. Fluid dynamic model predictions are compared to field and seismic observations. The research exercises LANL hydrodynamic codes and brings their operators into contact with a broader world of computational research. It supports related missions in treaty verification and hazard reduction.