This monograph presents the physical concepts and mathematical models related to the aerodynamic challenges of the environment, along with analytical and numerical methods for calculating unsteady spatial flows. It explores a wide range of problems in explosion theory, convection, and atmospheric dynamics. The text includes finite difference methods and results from computational experiments addressing various issues within these fields of aerohydrodynamics. Particular attention is given to flows initiated in the atmosphere by the rise of individual thermals and thermal ensembles, the interaction of explosive shock waves with different objects, and the formation of concentrated vortices akin to tornadoes. To aid in understanding the material, the monograph outlines fundamental concepts of continuum mechanics and frequently used mathematical models, including systems of equations in both integral and differential forms, as well as the difference methods that underpin the computational and subject-specific information presented. Written in an accessible style, this monograph is intended for a broad audience of researchers, graduate students, and undergraduates in related fields.