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Our goal in this work is to enable high fidelity computations of unsteady flowfields about complex geometries with moving bodies which may be accelerating with respect to each other, with applications to submarine and torpedo design, missile and aircraft design and engine and propulsor technology. Unstructured grid technology has tremendous potential for addressing such challenging CFD problems. An essential element of the CFD process for complex geometries is the construction of a discrete grid on which the field equations are represented in discrete form. Representative applications of both grid generation and flow solution will be used to demonstrate these capabilities.