Acoustic singular surfaces in an exponential class of inhomogeneous gases: A new numerical approach based on Krylov subspace spectral methodologies

TL;DR

This paper combines analytical and advanced numerical methods to study acoustic singular surfaces in exponentially varying inhomogeneous gases, demonstrating efficient and accurate simulation of wave propagation phenomena.

Contribution

It introduces a novel application of Krylov subspace spectral methods for simulating acoustic singular surfaces in inhomogeneous gases, improving accuracy and efficiency over traditional techniques.

Findings

KSS methods enable larger CFL numbers for faster computation.

KSS accurately captures wavefront features predicted by theory.

Analytical results detail the evolution of shock and acceleration waves.

Abstract

We investigate the propagation of acoustic singular surfaces, specifically, linear shock waves and nonlinear acceleration waves, in a class of inhomogeneous gases whose ambient mass density varies exponentially. Employing the mathematical tools of singular surface theory, we first determine the evolution of both the jump amplitudes and the locations/velocities of their associated wave-fronts, along with a variety of related analytical results. We then turn to what have become known as Krylov subspace spectral (KSS) methods to numerically simulate the evolution of the full waveforms under consideration. These are not only performed quite efficiently, since KSS allows the use of `large' CFL numbers, but also quite accurately, in the sense of capturing theoretically-predicted features of the solution profiles more faithfully than other time-stepping methods, since KSS customizes the computation of the components of the solution corresponding to the different frequencies involved. The presentation concludes with a listing of possible, acoustics-related, follow-on studies.