Novel Methods for Numerical Simulation of Wave Propagation in Inhomogeneous Media

Many types of waves propagate through inhomogeneous media, such as light waves propagating in the air, where the particle density depends on the height of the atmospheric layers, acoustic waves propagating in the water, where the salinity depends on the ocean depth, or seismic waves propagating in the earth, where the density of geological layers varies depending on their sedimentation history. The scientific thrust of this project is devoted to the development of numerical simulation tools for wave propagation in anisotropic and inhomogeneous media.

The principal application targeted is wave propagation in aeroacoustics to study the noise generated by a turbo-reactor in a flow, where the source of inhomogeneity and anisotropy is the non-uniform air flow around the engine. Yet the methods considered will also apply to other variable material properties such as permittivity or sound speed.

This project is concerned with the further development of a class of Trefftz-like methods. Trefftz methods rely, in broad terms, on the idea of approximating solutions to partial differential equations using local basis functions, which are exact solutions of the governing equation, making explicit use of information about the ambient medium. Instead, the new methods rely on basis functions that are approximate solutions of the governing equation rather than exact solutions.

The PI therefore refers to such methods as quasi-Trefftz methods. The goal of this project is two-fold: (1) investigate the properties of the quasi-Trefftz methods when using a high-order local basis; (2) investigate numerical integration techniques for the corresponding basis functions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.