A Lagrangian for Compressible Flow Focusing on Dissipation due to Thermal Conduction

Scholle, M.; Ismail‐Sutton, S.; Gaskell, P. H.

Abstract

With the aim of describing compressible viscous flows by means of a variational principle that takes into account heat conduction, a recently proposed Lagrangian is subjected to a detailed linear wave analysis that stems directly from the Lagrangian. The accompanying thermodynamic equation of state employed leads to a natural decomposition of the conduction term into three contributions, with the importance of each accessed through a detailed analysis employing a recently developed perturbation methodology giving rise to a favorable system of governing Jacobi equations. In addition to the model Lagrangian itself, three potential model scenarios—based on different combinations of the contributions forming the Lagrangian—are rigorously evaluated and appraised, regarding the occurrence, or otherwise, of dissipation recognizable by an attenuation of harmonic waves. Results reveal that two of the four models are suitable candidates, and suggest one in particular.

Citation

Scholle, M., Ismail‐Sutton, S., & Gaskell, P. H. (2025). A Lagrangian for Compressible Flow Focusing on Dissipation due to Thermal Conduction. Studies in Applied Mathematics, 154(1), Article e12791. https://doi.org/10.1111/sapm.12791

• Journal Article Type: Article
• Acceptance Date: Nov 3, 2024
• Online Publication Date: Nov 27, 2024
• Publication Date: Jan 1, 2025
• Deposit Date: Dec 2, 2024
• Publicly Available Date: Dec 2, 2024
• Journal: Studies in Applied Mathematics
• Print ISSN: 0022-2526
• Electronic ISSN: 1467-9590
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 154
• Issue: 1
• Article Number: e12791
• DOI: https://doi.org/10.1111/sapm.12791
• Keywords: variational calculus, dispersion relation, thermomechanical coupling, dissipation, wave attenuation
• Public URL: https://durham-repository.worktribe.com/output/3116069