Accelerating three-dimensional navier-stokes calculations

This paper addresses the widely observed breakdown in multigrid performance for turbulent Navier-Stokes computations on highly stretched meshes. Extending previous work in two dimensions, two alternative preconditioned multigrid methods are proposed based on an examination of the analytic expressions for the preconditioned Fourier footprints in an asymptotically stretched boundary layer cell. These methods provide for efficient multigrid performance by ensuring that all error modes are effectively damped inside the boundary layer. The schemes also strive to balance the trade-offs between operation count, storage overhead, and parallel scalability. The first of these methods is implemented for the present work and is shown to dramatically accelerate convergence for three-dimensional turbulent Navier-Stokes calculations.