Adaptive time step control for global-in-time Galerkin-Petrov discretizations of evolution equations in the context of incompressible flows
| dc.contributor.advisor | Turek, Stefan | |
| dc.contributor.author | Wambach, Lydia Carmen | |
| dc.contributor.referee | Schieweck, Friedhelm | |
| dc.date.accepted | 2025-04-10 | |
| dc.date.accessioned | 2025-10-02T05:49:54Z | |
| dc.date.available | 2025-10-02T05:49:54Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | The goal of adaptive time step control is to efficiently control the accuracy of a simulation. In terms of accuracy, a higher order time-stepping scheme is advantageous, although it results in a higher computational cost. In particular, High Performance Computing (HPC) focuses on efficient performance by using an ever-increasing number of cores and thus applying numerical schemes in parallel. Therefore, global-in-time adaptive time step control based on a higher order time discretization scheme is of interest, especially in the area of Computational Fluid Dynamics (CFD). In this work, we use the higher order continuous Galerkin-Petrov method as a time discretization scheme in a global-in-time adaptive time step control. The length of the time steps is controlled by so-called controllers based on error estimators. These errors are estimated by two approximations of the solution of different order. Here, we use a linear post-processing step from the continuous Galerkin-Petrov method with low computational cost to obtain a higher order solution. Although this is common in the literature on no-pressure problem types, we present a velocity and a new pressure error estimator for the Navier-Stokes equations. These error estimators approximate the analytic errors suitable, as we show for the heat equation and for incompressible flows as in the Navier- Stokes equations. Especially, for the flow around a cylinder benchmark for Newtonian and non-Newtonian fluids, we present error estimators for the lift and drag coefficients. All numerical tests in this thesis have been implemented in the FEAT3 software. We also introduce a new global-in-time adaptive strategy. This provides a time-parallel approach. In order to deepen this topic, we briefly introduce two existing global-in-time approaches and discuss a possible realization for the cGP(2) adaptive time-stepping, but no parallel numerical investigation is done. The new global-in-time adaptive strategy defines a new time grid in each adaptive iteration and computes the associated solution over the entire time interval. The classic step size controllers described in the literature are adapted to take into account error estimates for pressure, lift, and drag coefficients. Investigations and comparisons follow in the numerical studies for the different model problems, where advisable controllers are highlighted. | en |
| dc.identifier.uri | http://hdl.handle.net/2003/44015 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-25783 | |
| dc.language.iso | en | |
| dc.subject | Adaptive time step control | en |
| dc.subject | Continuous Galerkin-Petrov | en |
| dc.subject | Global-in-time | en |
| dc.subject | Incompressible flows | en |
| dc.subject.ddc | 510 | |
| dc.subject.rswk | Galerkin-Methode | de |
| dc.subject.rswk | Fluss <Mathematik> | de |
| dc.subject.rswk | Navier-Stokes-Gleichung | de |
| dc.subject.rswk | Fluid | de |
| dc.subject.rswk | AMG <Mathematik> | de |
| dc.title | Adaptive time step control for global-in-time Galerkin-Petrov discretizations of evolution equations in the context of incompressible flows | en |
| dc.type | Text | |
| dc.type.publicationtype | PhDThesis | |
| dcterms.accessRights | open access | |
| eldorado.dnb.deposit | true | |
| eldorado.secondarypublication | false |