On the application of Krylov subspace spectral methodologies to poroacoustic shock formation in an exponential class of inhomogeneous gases

Abstract

In this communication, the propagation of poroacoustic acceleration waves in a class of inhomogeneous gases whose ambient mass density varies exponentially is considered. Employing the 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 simulations 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, since KSS customizes the computation of the components (of a solution) corresponding to the different frequencies involved. The presentation concludes with a discussion of possible acoustics-related follow-on studies.