Numerical Factorization of Propagation Operator for Hyperbolic Equations and Application to One-way, True Amplitude One-way Equations and Bremmer Series

This paper presents a purely numerical factorization of the propagation operator for a generic hyperbolic equation, based on the work of Towne & Colonius in 2015, that does not require heavy analytical development. This method is applied to form one-way equations with the objective of computing the propagation of waves inside a medium. The main advantage of this formulation is that pseudo eigenvectors and eigenvalues matrices are built, leading to the possibility to use the one-way equations into a true amplitude formalism and/or inside a Bremmer series. These two methods allow an extension of the domain of application of the one-way equations when the medium of propagation presents variations along the privileged direction. In particular, these formulations allow to take into account the phenomena of reflection and refraction of the incident wave. Finally numerical results are presented on different 2D situations based on the linearized Euler equations and compared to the results obtained with a full wave resolution. The issues of both the accuracy and the requirements in computational resources of the one-way resolution are also addressed.