Robust, segregated time integration for direct numerical simulation of low-Mach, variable-density, turbulent flows

For the direct numerical simulation of flows in unbounded domains, explicit time discretization is attractive since the timestep required for accuracy is similar to that required for stability. However, due to redundancy in the variable-density Navier-Stokes equations, advancing the equations using a segregated scheme can lead to destabilizing inconsistencies between the scalar and momentum fields. We demonstrate how the redundancy can be eliminated and formulate a matrix-free, iterative scheme which converges to the solution of this ``collapsed'' problem under certain conditions. In the context of pseudospectral DNS, this allows massively parallel algorithms to be used while making the method more robust to flows with large density variations. The DNS formulation is an extension of the incompressible Navier-Stokes formulation of Kim, Moin, and Moser (1987) to the variable-density context by utilizing a Helmholtz decomposition of the momentum. Results shown explore the stability and order of the scheme and its application to a Rayleigh-Taylor instability problem.