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Efficient scalable solvers for incompressible flow problems
 Mitro, Erik ; Hron, Jaroslav (advisor) ; Rozložník, Miroslav (referee)
In this thesis, the different solution methods for saddle-point systems aris- ing from fluid dynamics are studied. The main emphasis is on Krylov subspace methods with effective preconditioning techniques for saddle-point systems ob- tained from finite element discretization of the Navier-Stokes equations. Two preconditioning techniques are presented: pressure-convection-diffusion precon- ditioning (PCD) and least-square commutator preconditioning (LSC). Both pre- conditioners are validated on two benchmarks: lid-driven cavity and flow around cylinder. From the computational point of view, we focus on comparing the performance of used solvers, with emphasis on our implementation of PCD pre- conditioning. All numerical simulations are performed by software Firedrake. 1
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