Projection method for the fluctuating hydrodynamics equations

Computational fluctuating hydrodynamics aims at understanding the impact of thermal fluctuations on fluid motions small scales through numerical exploration. These are modeled as stochastic flux terms and incorporated into classical Navier-Stokes equations, which need to be solved numerically. In this paper, we present a novel projection-based method for solving incompressible (FHD) equations. By analyzing equilibrium structure factor spectrum velocity field linearized FHD investigate how inherent splitting errors affect solution partial differential equations in presence non-periodic boundary conditions, iterative corrections can reduce these errors. Our computational examples demonstrate both capability our approach reproduce correctly properties fluids well its potential use simulations multi-physics problems.