Abstract: A framework to create new specific analytical solutions of the equations of motion for hyperbolic boundary value problems is presented. The method relies on a closed-form integral equation for mass density, involving a term that combines sources, geometry, ambient values, and radiation. Products of the density integral result in new more complicated solutions. The density field is used to recover the field variables in the near-field through far-field relative to the aerodynamic body. The aerodynamic body is modeled as a product and combination of generalized functions. Thus, resultant analytical solutions are also a combination of generalized functions. Derivations of time-dependent analytical solutions and example predictions are presented in one and two spacial domains. Cases examined for Euler equations include moving shock waves, oblique shock waves, Prandtl-Meyer expansions, and fields from more complicated bodies. A discussion of limitations and future directions of the methodology is included. The methodology, in a more complicated form, is used primarily for hypersonic sonic boom prediction.
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