Explicit-Iterative Scheme for the Time Integration of a System of Navier–Stokes Equations

Abstract

We propose a new explicit-iterative scheme for time integrating the multidimensional Navier–Stokes equations of a compressible environment through splitting into convective and diffusive stages, which are performed sequentially at each time step. The convective stage is implemented using the Godunov scheme; and the diffusive stage, using the Chebyshev explicit-iterative LI-M scheme, which has no restriction on the time step. The resulting scheme ensures that the basic conservation laws hold on arbitrary irregular grids. The explicit nature of the calculations ensures that the scheme can be efficiently used in various parallel technologies.