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

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