Exact domain truncation for the Morse-Ingard equations

TL;DR

This paper develops an exact nonlocal boundary condition for the Morse-Ingard equations, enabling accurate and efficient numerical solutions for modeling trace gas sensors on small computational domains.

Contribution

It adapts a nonlocal boundary condition from Helmholtz problems to the coupled Morse-Ingard system, ensuring convergence to the true solution with coarse meshes.

Findings

Exact boundary condition improves accuracy on small domains

Galerkin discretization converges to the true solution

GMRES solver with local preconditioner is effective

Abstract

Morse and Ingard give a coupled system of time-harmonic equations for the temperature and pressure of an excited gas. These equations form a critical aspect of modeling trace gas sensors. Like other wave propagation problems, the computational problem must be closed with suitable far-field boundary conditions. Working in a scattered-field formulation, we adapt a nonlocal boundary condition proposed earlier for the Helmholtz equation to this coupled system. This boundary condition uses a Green's formula for the true solution on the boundary, giving rise to a nonlocal perturbation of standard transmission boundary conditions. However, the boundary condition is exact and so Galerkin discretization of the resulting problem converges to the restriction of the exact solution to the computational domain. Numerical results demonstrate that accuracy can be obtained on relatively coarse meshes on small computational domains, and the resulting algebraic systems may be solved by GMRES using the local part of the operator as an effective preconditioner.