AiryModell

AiryModell is a computational framework used to model wave propagation in stratified or inhomogeneous media. Named for its use of Airy-function based corrections near turning points, the model provides a semi-analytic approach to approximate solutions of the governing wave equation with slowly varying properties.

Formulation and computation: The model expresses the wave field as a product of a slowly varying envelope and an Airy-based correction term. The governing equation is reduced to a set of coupled ordinary differential equations for the envelope, which are solved with boundary conditions appropriate to the problem. The method supports flexible parameterization of the medium's index of refraction, density, or impedance, and is amenable to efficient numerical implementation on standard CPUs.

Applications: It has been applied in atmospheric acoustics to predict downwind sound propagation, in seismology for mantle wave scattering, and in optics for graded-index waveguides where the refractive index changes gradually.

History and development: AiryModell was introduced in 2015 by a consortium of researchers led by Dr. Anika Mueller and Dr. Paolo Ricci. Since then it has been implemented in open-source simulation toolkits and cited in several peer-reviewed studies.

Limitations and scope: The model assumes smooth variations and moderate frequencies; sharp discontinuities or nonlinear effects may require alternative methods. Its accuracy depends on the validity of the slowly varying envelope assumption and the accuracy of the boundary conditions.

See also: Airy function; WKB approximation; gradient-index optics; wave equation.