  A novel algorithm for the direct numerical simulation of the
variable-density, low-Mach Navier-Stokes equations extending the method of Kim,
Moin, and Moser (1987) for incompressible flow is presented here. A Fourier
representation is employed in the two homogeneous spatial directions and a
number of discretizations can be used in the inhomogeneous direction. The
momentum is decomposed into divergence- and curl-free portions which allows the
momentum equations to be rewritten, removing the need to solve for the
pressure. The temporal discretization is based on an explicit, segregated
Runge-Kutta method and the scalar equations are reformulated to directly
address the redundancy of the equation of state and the mass conservation
equation. An efficient, matrix-free, iterative solution of the resulting
equations allows for second-order accuracy in time and numerical stability for
large density ratios, which is demonstrated for ratios up to $\sim 25.7$.
