Abstract
The Morse–Ingard equations of thermoacoustics Morse and Ingard (1986) are a system of coupled time-harmonic equations for the temperature and pressure of an excited gas. They form a critical aspect of modeling trace gas sensors. In this paper, we analyze a reformulation of the system that has a weaker coupling between the equations than the original form. We give a Gårding-type inequality for the system that leads to optimal-order asymptotic finite element error estimates. We also develop preconditioners for the coupled system. These are derived by writing the system as a 2 × 2 block system with pressure and temperature unknowns segregated into separate blocks and then using either the block diagonal or block lower triangular part of this matrix as a preconditioner. Consequently, the preconditioner requires inverting smaller, Helmholtz-like systems individually for the pressure and temperature. Rigorous eigenvalue bounds are given for the preconditioned system, and these are supported by numerical experiments.
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