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Preconditioned multigrid methods for compressible flow calculations on stretched meshes. (English) Zbl 0893.76061
The authors propose and test efficient preconditioned multigrid methods for solving conservation equations of fluid mechanics for inviscid and viscous flows. The improvement of the solution technique rests on the observation that a block-Jacobi matrix preconditioner substantially improves the damping and propagative efficiency of Runge-Kutta time-stepping schemes when used on coarse grids. For solutions of the Euler equations, the convergence rate is improved by a factor of three to five; solutions of the Navier-Stokes equations for two-dimensional turbulent flows, obtained on highly stretched meshes, are shown to yield a factor of ten to forty of improvement in the convergence rate.
Reviewer: E.Krause (Aachen)

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
Software:
Mathematica
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