Many of the fluid and solid dynamics phenomena studied experimentally at GALCIT are also being investigated by numerical simulation and by theoretical analysis. Computational mechanics is a key area that underpins the research activities at GALCIT. Present active research areas in computational techniques include direct numerical simulation of both fluid mechanics; advanced methods for flow high performance simulation; new algorithms and sub-grid-scale models for compressible and incompressible flows; large-eddy simulation methods; analytical and computational techniques for turbulence structure diagnostics; analysis of turbulent mixing dynamics; high-explosive interactions with deformable boundaries, hypersonic flow; non-equilibrium molecular dynamics simulations for probing breakdown of continuum models, and computational flow control. Our research activities in computational solid mechanics address phenomena ranging from the atomistic scale, e.g., nano-indentation, to the structural scale, e.g., fracture of aircraft or spacecraft components, modeling of large space structures or even dynamic fragmentation phenomena accompanying hypervelocity impact. It provides an indispensable tool for understanding the relation between structure and mechanical properties of materials, for predicting the efficiency of such industrial processes as machining and metal forming, and for assessing the safety of such structures as airplanes, spacecraft, automobiles, and bridges. Ongoing efforts focus on development of numerical methods and large-scale simulations, as well as use of Bayesian estimation and Machine-Learning approaches to improve and extend sub-grid-scale modeling.