Explicit time integration of the Navier–Stokes equations using the local iteration method

New time integration algorithm LI-M is proposed for the Navier–Stokes equations of compressible heat-conducting flows. This algorithm is based on the splitting procedure by convection and diffusion processes over a time step. The explicit scheme computes solution of convection part and the explicit-iteration Chebyshev scheme computes the diffusion part. The resulting scheme makes it possible to avoid diffusion restriction on time step. The scheme has a predictor-corrector structure and ensures the fulfillment of conservation laws. The explicit nature of the calculations ensures the efficiency of the use of the scheme in various parallel technologies.