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Krylov subspace methods in computational fluid dynamics. (English) Zbl 1063.76081

Summary: Nearly every discretization technique in computational fluid dynamics leads – in the end – to the subproblem to solve linear systems. Thus, it is clear that the efficient solution of linear systems plays a crucial role for numerical simulations in general. Frequently, for steady problems one has to solve at least one large, sparse, and often unsymmetric linear system, and for unsteady problems such systems arise in every time step. Here, we present a survey on recent Krylov subspace methods for the solution of linear systems and elucidate their numerical behavior and effects with regard to discretization matrices which arise from different discretization techniques for convection-diffusion problems as well as for the Euler equations.

MSC:

76M99 Basic methods in fluid mechanics
65F10 Iterative numerical methods for linear systems
76N15 Gas dynamics (general theory)
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