Approximation of a simple Navier-Stokes model by monotonic rearrangement

TL;DR

This paper introduces a novel approximation method for a one-dimensional compressible Navier-Stokes model using a time-discrete scheme that combines stochastic differential equations with monotonic rearrangement, extendable to related systems.

Contribution

It presents a new approximation approach for the Navier-Stokes model employing stochastic discretization and rearrangement, enhancing numerical methods for fluid dynamics.

Findings

Effective approximation of the Navier-Stokes model

Extension to Navier-Stokes-Poisson system

Potential for improved numerical schemes

Abstract

We consider a Navier-Stokes model for compressible fluids in one space dimension. We show that it can be approximated by a time-discrete scheme combining the discretization of a trivial stochastic differential equation and the application of a suitable monotonic rearrangement operator In addition, our result can be easily extended to a related Navier-Stokes-Poisson system.