  We formulate and study computationally the fluctuating compressible
Navier-Stokes equations for reactive multi-species fluid mixtures. We contrast
two different expressions for the covariance of the stochastic chemical
production rate in the Langevin formulation of stochastic chemistry, and
compare both of them to predictions of the chemical Master Equation for
homogeneous well-mixed systems close to and far from thermodynamic equilibrium.
We develop a numerical scheme for inhomogeneous reactive flows, based on our
previous methods for non-reactive mixtures [K. Balakrishnan, A. L. Garcia, A.
Donev and J. B. Bell, Phys. Rev. E 89:013017, 2014]. We study the suppression
of non-equilibrium long-ranged correlations of concentration fluctuations by
chemical reactions, as well as the enhancement of pattern formation by
spontaneous fluctuations. Good agreement with available theory demonstrates
that the formulation is robust and a useful tool in the study of fluctuations
in reactive multi-species fluids. At the same time, several problems with
Langevin formulations of stochastic chemistry are identified, suggesting that
future work should examine combining Langevin and Master Equation descriptions
of hydrodynamic and chemical fluctuations.
