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Abstract

Boussinesq theory can model quite accurately viscous flows that involve multiple fluids with interfaces between them, so long as there is not much difference between the densities of the various fluids. However, the Boussinesq approximation is generally poor when the density ratio between the fluids is large. Here, we propose an Extended Boussinesq approximate equation, that allows for large density ratios, while still remaining straightforward to implement. Examples are given for planar Rayleigh–Taylor instability, where the Boussinesq and the novel Extended Boussinesq models are compared with the predictions of an SPH fluid dynamics code, to confirm this approach.

Item Type:	Article
Authors/Creators:	Forbes, LK and Turner, RJ and Walters, SJ
Keywords:	Boussinesq model, extended Boussinesq model, fluid interface, Rayleigh–Taylor instability
Journal or Publication Title:	Journal of Engineering Mathematics
Publisher:	Kluwer Academic Publ
ISSN:	0022-0833
DOI / ID Number:	https://doi.org/10.1007/s10665-022-10215-w
Copyright Information:	© The Author(s) 2022 This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
Related URLs:	Google Scholar: Forbes, LK UTAS Profile: Forbes, LK UTAS Profile: Turner, RJ
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