A semi-coarsened multigrid solver for the Euler and Navier-Stokes equations with local preconditioning

An optimization formulation is described for multistage schemes based on the hi-hi high-frequency content in the Fourier footprint of the preconditioned spatial operator. These coefficients, when used in conjunction with semi-coarsened multigrid and local preconditioning provide a fast and robust method for achieving steady-state Euler solutions. Multigrid speed-ups of 3-4 times are observed when using local preconditioning as compared to local time-stepping. The extension to Navier-Stokes operators is also described.

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