A Hamiltonian interacting particle system for compressible flow

Simon Hochgerner

doi:10.3390/w12082109

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arXiv · 2007.13692

A Hamiltonian interacting particle system for compressible flow

Simon Hochgerner

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Abstract

The decomposition of the energy of a compressible fluid parcel into slow (deterministic) and fast (stochastic) components is interpreted as a stochastic Hamiltonian interacting particle system (HIPS). It is shown that the McKean-Vlasov equation associated to the mean field limit yields the barotropic Navier-Stokes equation with density dependent viscosity. Capillary forces can also be treated by this approach. Due to the Hamiltonian structure the mean field system satisfies a Kelvin circulation theorem along stochastic Lagrangian paths.

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Simon Hochgerner. 2020-07-27. A Hamiltonian interacting particle system for compressible flow. https://doi.org/10.3390/w12082109

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