A Hamiltonian interacting particle system for compressible flow

TL;DR

This paper introduces a Hamiltonian interacting particle system framework for modeling compressible fluid flow, linking stochastic particle interactions to classical fluid equations and preserving key physical properties.

Contribution

It presents a novel stochastic Hamiltonian particle system approach that derives the barotropic Navier-Stokes equations with density-dependent viscosity from mean field limits.

Findings

The mean field limit yields the barotropic Navier-Stokes equation.

Capillary forces can be incorporated into the Hamiltonian framework.

The system satisfies a Kelvin circulation theorem along stochastic paths.

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.