A Hamiltonian interacting particle system for compressible flow
Fluid Dynamics
2020-10-02 v2 Mathematical Physics
math.MP
Symplectic Geometry
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.
Cite
@article{arxiv.2007.13692,
title = {A Hamiltonian interacting particle system for compressible flow},
author = {Simon Hochgerner},
journal= {arXiv preprint arXiv:2007.13692},
year = {2020}
}
Comments
v2: fixed a few typos