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