Branching Paths Statistics for confined Flows : Adressing Navier-Stokes Nonlinear Transport

TL;DR

This paper extends probabilistic branching path methods to Navier-Stokes nonlinear transport, enabling new simulation techniques for confined fluid flows.

Contribution

It introduces a novel framework integrating branching stochastic processes with Navier-Stokes equations for better fluid flow modeling.

Findings

Developed new propagator representations for fluid dynamics.

Proposed backward Monte Carlo algorithms for efficient simulations.

Extended path-space probabilistic methods to nonlinear Navier-Stokes transport.

Abstract

Recent advances have allowed to tackle exact path-space probabilistic representations of macroscopic advection-diffusion models involving advection nonlinearities by step forward approaches in terms of continuous branching stochastic processes. Yet, the need of such paradigm shift is huge for the broad flied of fluid flows. In deed, wherever for climate dynamics, engeenering, geophysical and planetary formations, or biomedical applications, complex transport phenomena involving diffusion and advection in confined domains set the physics. In this work, we advance this framework by casting such branching representations within the class of Navier-Stokes strongly nonlinear transport. This yields novel propagator representations for fluid dynamics and opens new routes for efficient simulations of fluids in confined domains by use of new Backward Monte Carlo algorithms.