An extended Boussinesq theory for interfacial fluid mechanics

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.