New Conservation Laws Based on Generalised Reynolds Transport Theorems

Robert K. Niven, Laurent Cordier, Eurika Kaiser, Michael Schlegel, Bernd R.
2020 Proceedings of the 22nd Australasian Fluid Mechanics Conference AFMC2020   unpublished
The Reynolds transport theorem gives a generic conservation law for a conserved quantity carried by fluid flow through a continuous control volume, providing the foundation for all conservation laws of fluid mechanics. We present new spatial and parametric multivariate generalisations of this theorem, each of which provides a continuous mapping of the contents of a domain within a coordinate space. The most general form involves mappings on a manifold, presented in a multivariate extension of
more » ... terior calculus. These theorems are used to generate tables of new conservation laws in integral form in different spaces, including Eulerian velocity space and velocity-volume phase space, based on fluid densities defined in these spaces.
doi:10.14264/380a993 fatcat:5qqcg4imsncmxfc4j4xbu56wcu