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engPollul, BernhardReusken, ArnoldIterative solvers in implicit time integration for compressible flowsinfo:eu-repo/classification/ddc/510Numerische StrömungssimulationKompressible StrömungNummerierungPräkonditionierungKrylov-VerfahrenNewton-VerfahrenQuasi-Newton-VerfahrenAutomatische DifferentiationNichtlineare GleichungLineare GleichungFinite-Volumen-MethodeMathematikSchrittweitensteuerungmatrixfreie MethodenQUADFLOWcomputational fluid dynamicsNewton-Krylovpseudo-transient continuationreordering techniquesCFL evolution strategiesComputational fluid dynamics (CFD) that was started in the 1960's is still an up-to-date research topic. In the Collaborative Research Center SFB~401 "Modulation of flow and fluid-structure interaction at airplane wings" being concerned with fundamental problems of high capacity aircrafts in transonic conditions, one key issue is the development of a new adaptive finite volume flow solver called QUADFLOW. Therein, certain iterative methods that arise in most CFD simulations are used for the simulation of compressible flow around an airfoil. QUADFLOW is designed for the stationary and non-stationary compressible Euler and Navier-Stokes equations. In this thesis we discuss the QUADFLOW solver and give an introduction to iterative methods. In the main part we discuss known and new preconditioners, numbering techniques, time step evolution strategies, and matrix-free methods. In this thesis an implicit time integration scheme is used. In case of a stationary problem this approach is called "pseudo-transient continuation", that is, one applies a time integration method to the unsteady Euler equations and the corresponding non-stationary solution converges to the stationary solution for time tending to infinity. This then yields a non-linear system of equations in each time step which is solved by a Newton-Krylov method. Therein one applies a linearization technique combined with a preconditioned Krylov subspace algorithm for solving the resulting linear problems. Our inexact Newton method uses a first order approximation of the Jacobian. The computational work for solving the large sparse systems in the applied Newton-Krylov method determines to a large extent the total computing time. In general for stationary problems this issue plays a bigger role than for non-stationary problems resulting from the choice of larger time step sizes during the computation. Therefore, we focus on the stationary Euler equations in this thesis. In this thesis different so-called "point-block" preconditioners are investigated and compared. Preconditioning is crucial for the convergence of the Krylov solver. Preconditioners strongly depend on the ordering of the cells of the Jacobian. We present a new odering that is based on a reduced matrix graph. Our new ordering can significantly improve robustness and corresponding computational time. The selection of the time step size in the implicit time integration is crucial for the numerical simulation. We compare two known time step evolution methods with a new strategy. The parameters that correspond to each of the strategies are investigated in a systematic parameter study. Furthermore we present a new strategy that selects the CFL number in such a way that the residual decreases as much as possible in every time step. We show that this strategy gives good results for a limited number of time steps but is usually slow compared with any of the standard CFL evolution strategies in the long run. A further acceleration of the time integration can be achieved by the use of a second order accurate Jacobian. Because the stencils for second order methods are usually quite large resulting in a complex Jacobian requiring much memory, we present a second order matrix-free method. For the implementation we use automatic differentiation providing a robust and reliable scheme that has better convergence properties compared with a corresponding divided differencing method. Using the second order matrix-free evaluation of the matrix-vector product the corresponding computational time can be significantly decreased.Aachen : Publikationsserver der RWTH Aachen University 194 S. : graph. Darst. (2008). = Aachen, Techn. Hochsch., Diss., 2008info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersionPublikationsserver der RWTH Aachen University2008info:eu-repo/semantics/openAccessDEhttps://publications.rwth-aachen.de/record/50412https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112958%22StudentsStudent Financial Aid ProvidersTeachersResearchersinfo:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-25974