As the world adopts cleaner and/or renewable energy sources, energy fluids (e.g. hydrogen, ammonia, liquefied natural gas, liquid air, etc.), their transport, and their storage are becoming increasingly important. Feed/product flows, flashing recirculation flows, evaporation, condensation, heat leak, and boil-off gas removal lead to state transients in their storage systems with significant mechanical, safety, environmental, and efficiency implications. This study presents a comprehensive simulation model based on a novel stretchable and spatially moving grid for predicting spatiotemporal transients in a cylindrical storage tank. The model is fully validated under limiting scenarios and then applied to several industrial storage terminals involving liquid hydrogen, liquid air, and liquefied natural gas. In addition to its novel grid formulation, the model offers significant advances over simpler lumped-parameter and complex fluid dynamics models in the literature and commercial process simulators. It gives useful practical insights into boil-off gas removal, pressure management, evaporation/condensation, and compressor sizing/operation.