Abstract
Applying operator splitting methods to the numerical simulation of compressible or incompressible viscous flows leads to the solution of Stokes type linear problems and of nonlinear elliptic systems. Once discretized, these problems involve a large number of variables and therefore require efficient solution methods.
In this paper, we discuss the solution of the Stokes subproblems by iterative methods preconditioned by a well chosen boundary operator. The nonlinear subproblems (which are highly advective) are solved by an iterative method of GMRES type (cf. [1]). Numerical results corresponding to the simulation of flow around (and/or inside) air intakes and bodies illustrate the possibilities of the methods discussed here.
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Bristeau, M.O., Glowinski, R., Periaux, J. (1989). Acceleration Procedures for The Numerical Simulation of Compressible and Incompressible Viscous Flows. In: Doltsinis, I.S. (eds) Advances in Computational Nonlinear Mechanics. International Centre for Mechanical Sciences, vol 300. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2828-2_6
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DOI: https://doi.org/10.1007/978-3-7091-2828-2_6
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