2016/08/08 by P. Stubbe, Peter Stubbe, Stubbe, Peter
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1608.02526
arxiv created 2016/08/08 · openalex publication_date 2016/08/08 · arxiv updated 2016/08/09 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28
The Euler and Navier-Stokes equations both belong to a closed system of three transport equations, describing the particle number density N, the macroscopic velocity v and the temperature T. These sytems are complete, leaving no room for any additional equation. Nonetheless, it is common practice in parts of the literature to replace the thermal equation by the incompressibility condition div v = 0, motivated by the wish to obtain simpler equations. It is shown that this procedure is physically inconsistent in several ways, with the consequence that incompressibility is not a property that can be enforced by an external condition. Incompressible behaviour, if existing, will have to follow self-consistently from the full set of transport equations.