Incremental pressure correction method for high-performance simulations of subsonic compressible flows

In the present work, we propose a time-splitting method to handle the treatment of pressure-velocity coupling in the context of subsonic compressible flows. We extend the well-known incremental pressure correction method for incompressible flows to subsonic compressible flows by solving, at each time step and for the temporal pressure increment variable, an elliptic equation involving a linear term. The governing equations, written in primitive variables, consist of the compressible Navier–Stokes equations along with the energy conservation equation. Closure with any chosen fluid equation of state enables the calculation of relevant thermophysical fluid properties. After deriving the proposed method and recalling its non-incremental counterpart, spatial and temporal second-order convergence are measured for both methods on various verification test cases. The classical pressure accuracy limitations of the non-incremental method for incompressible flows are overcome when applied to compressible subsonic flows due to the different nature of the pressure equation. The incremental method is subsequently applied to steady and unsteady high-gradient temperature and density flows, i.e. beyond the Boussinesq approximation known as Non-Oberbeck-Boussinesq flows, such as thermoacoustic wave propagation and natural convection problems. Both verification and validation processes are systematically and carefully detailed. Finally, Direct Numerical Simulation of three-dimensional compressible Rayleigh–Bénard turbulent convection of highly compressible fluid supercritical carbon dioxide is proposed. The parallel implementation efficiency of the method is also reported throught strong and weak scalability tests in the last three-dimensional case up to 131,072 cores. We demonstrate the capacity to provide a full second-order accurate and efficient incremental pressure correction method to solve subsonic compressible flows.