An additive turbulent decomposition of the Navier-Stokes equations implemented on highly parallel computer systems

Progress is reported on a study of a new turbulence simulation technique based on an unaveraged, additive decomposition of the Navier-Stokes equations. The decomposition provides a natural separation of the governing equations into large- and small-scale parts, with the small scale solved on local subdomains to provide a high degree of parallelism. Results presented here include formal consistency and accuracy proofs for Burgers' and the full 3-D, incompressible Navier-Stokes equations, as well as various details of transferring information between the large- and small-scale calculations. Initial work on applying the method to the study of transition to turbulence in circular pipe flow is also documented. In addition, studies on the domain decomposition and multigrid aspects of the method, using the Schwarz alternating method and the full-approximation scheme, is included.