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A novel algorithm for the direct numerical simulation of thevariable-density, low-Mach Navier-Stokes equations extending the method of Kim,Moin, and Moser (1987) for incompressible flow is presented here. A Fourierrepresentation is employed in the two homogeneous spatial directions and anumber of discretizations can be used in the inhomogeneous direction. Themomentum is decomposed into divergence- and curl-free portions which allows themomentum equations to be rewritten, removing the need to solve for thepressure. The temporal discretization is based on an explicit, segregatedRunge-Kutta method and the scalar equations are reformulated to directlyaddress the redundancy of the equation of state and the mass conservationequation. An efficient, matrix-free, iterative solution of the resultingequations allows for second-order accuracy in time and numerical stability forlarge density ratios, which is demonstrated for ratios up to $\sim 25.7$.

A pseudospectral method for direct numerical simulation of low-Mach, variable-density, turbulent flows