Meshfree method for fluctuating hydrodynamics

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.