A non-conventional discontinuous Lagrangian for viscous flow

Scholle, M.; Marner, F.

Abstract

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.

Citation

Scholle, M., & Marner, F. (2017). A non-conventional discontinuous Lagrangian for viscous flow. Royal Society Open Science, 4(2), Article 160447. https://doi.org/10.1098/rsos.160447

• Journal Article Type: Article
• Acceptance Date: Jan 4, 2017
• Online Publication Date: Feb 8, 2017
• Publication Date: Feb 8, 2017
• Deposit Date: Jul 25, 2017
• Publicly Available Date: Jul 25, 2017
• Journal: Royal Society Open Science
• Electronic ISSN: 2054-5703
• Publisher: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 4
• Issue: 2
• Article Number: 160447
• DOI: https://doi.org/10.1098/rsos.160447
• Public URL: https://durham-repository.worktribe.com/output/1351289