Meshfree method for fluctuating hydrodynamics

TL;DR

This paper develops a meshfree Lagrangian particle method for fluctuating hydrodynamics based on LLNS equations, accurately capturing thermal fluctuations and shock dynamics, validated against theoretical and numerical benchmarks.

Contribution

It introduces a novel meshfree particle approach for LLNS equations that effectively models thermal fluctuations and shock behavior in hydrodynamic systems.

Findings

Accurately reproduces equilibrium variance and correlations.

Successfully captures shock location in random walk tests.

Validates method against theoretical fluctuation-dissipation predictions.

Abstract

In the current study a meshfree Lagrangian particle method for the Landau-Lifshitz Navier-Stokes (LLNS) equations is developed. The LLNS equations incorporate thermal fluctuation into macroscopic hydrodynamics by the addition of white noise fluxes whose magnitudes are set by a fluctuation-dissipation theorem. The study focuses on capturing the correct variance and correlations computed at equilibrium flows, which are compared with available theoretical values. Moreover, a numerical test for the random walk of standing shock wave has been considered for capturing the shock location.