Integral equation methods for the Morse-Ingard equations

• Published in: Journal of computational physics Vol. 492; p. 112416
• Main Authors: Wei, Xiaoyu, Klöckner, Andreas, Kirby, Robert C.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.11.2023
• Subjects: Fast multipole method; Integral equation method; Quadrature-by-expansion; The Morse-Ingard equations; Fast multipole method; The Morse-Ingard equations; Quadrature-by-expansion; Integral equation method
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2023.112416

We present two (a decoupled and a coupled) integral-equation-based methods for the Morse-Ingard equations subject to Neumann boundary conditions on the exterior domain. Both methods are based on second-kind integral equation (SKIE) formulations. The coupled method is well-conditioned and can achieve high accuracy. The decoupled method has lower computational cost and more flexibility in dealing with the boundary layer; however, it is prone to the ill-conditioning of the decoupling transform and cannot achieve as high accuracy as the coupled method. We show numerical examples using a Nyström method based on quadrature-by-expansion (QBX) with fast-multipole acceleration. We demonstrate the accuracy and efficiency of the solvers in both two and three dimensions with complex geometry. •We propose two novel SKIE formulations for the Morse-Ingard equations.•We solve on an exterior domain with sound-hard boundary conditions to model trace gas sensors.•We can impose Sommerfeld-like radiation conditions at infinity without domain truncation.•We discretize using a Nyström method based on quadrature-by-expansion (QBX) with fast-multipole acceleration.•We demonstrate compatibility of our methods with high order discretization over complex geometries.