Verifikationsmethodik für die rechnerische Windtechnik Vorhersage von Windlasten an Tragwerken

In this thesis, a new credibility assessment framework is developed for computational wind engineering (CWE) simulations. The framework is mainly developed for testing code implementation correctness and estimation of the discretization uncertainty for eddy-resolving, and unsteady simulations. The framework is composed of two main milestones. First, a modular and flexible procedure for code verification is developed with the ability of testing black box codes. The code verification procedure focuses on the consistency of the code implementation and convergence of field variables. The procedure for code verification consists of analytical benchmarks, either exact or manufactured, with increasing complexity to test the implementation of each term in the Navier-Stokes equation. Second, the credibility assessment framework has a guideline for the quantification of discretization error/uncertainty. More precisely, guidelines are defined for solution verification. The discretization error/uncertainty estimation is based on Richardson Extrapolation approach. A solution biased uncertainty estimator is used to account for using unstructured grids, non-uniform refinement, and non-asymptotic solutions. The newly developed framework has a new definition for the measurement of grid size, handling simulation data with anomalous behavior, and for the safety factor definition in the uncertainty quantification of the discretization error. The assessment methodology is suited to both well- and ill-behaved sequences of simulations. The performance of the assessment methodology is checked with a glimpse on validation with experimental data. Finally, it can be concluded that the developed verification methodology is highly qualified to judge the quality of CWE simulations. Moreover, the generality and modularity of the framework makes it applicable to any software environment regardless of the discretization scheme. Consequently, the methodology encourages further research on the identification of the reliability of CWE simulations.In dieser Arbeit wird ein neues Rahmenwerk zur Glaubwürdigkeitsbewertung für rechnergestützte Windsimulationen (CWE) entwickelt. Der Rahmen wird hauptsächlich für die Prüfung der Korrektheit der Code-Implementierung und die Abschätzung der Diskretisierungsunsicherheit für wirbelauflösende und instationäre Simulationen entwickelt. Das Framework besteht aus zwei Hauptmeilensteinen. Erstens wird ein modulares und flexibles Verfahren zur Code-Verifikation entwickelt, das die Möglichkeit bietet, Black-Box-Codes zu testen. Das Code-Verifikationsverfahren konzentriert sich auf die Konsistenz der Code-Implementierung und die Konvergenz der Feldvariablen. Das Verfahren zur Codeverifizierung besteht aus analytischen Benchmarks, entweder exakt oder hergestellt, mit zunehmender Komplexität, um die Implementierung jedes Terms in der Navier-Stokes-Gleichung zu testen. Zweitens verfügt das Rahmenwerk zur Glaubwürdigkeitsbewertung über einen Leitfaden zur Quantifizierung von Diskretisierungsfehlern/Unsicherheiten. Genauer gesagt, werden Richtlinien für die Verifizierung der Lösung definiert. Die Schätzung des Diskretisierungsfehlers/der Unsicherheit basiert auf dem Richardson-Extrapolationsansatz. Ein lösungsverzerrter Unsicherheitsschätzer wird verwendet, um die Verwendung unstrukturierter Gitter, ungleichmäßiger Verfeinerung und nicht asymptotischer Lösungen zu berücksichtigen. Der neu entwickelte Rahmen hat eine neue Definition für die Messung der Gittergröße, die Behandlung von Simulationsdaten mit anomalem Verhalten und für die Definition des Sicherheitsfaktors bei der Unsicherheitsquantifizierung des Diskretisierungsfehlers. Die Bewertungsmethodik eignet sich sowohl für gut als auch für schlecht verhaltene Simulationsfolgen. Die Leistungsfähigkeit der Bewertungsmethodik wird mit einem Blick auf die Validierung mit experimentellen Daten überprüft. Abschließend kann festgestellt werden, dass die entwickelte Verifikationsmethodik hoch qualifiziert ist, um die Qualität von CWE-Simulationen zu beurteilen. Darüber hinaus macht die Allgemeingültigkeit und Modularität des Rahmens es für jede Softwareumgebung unabhängig vom Diskretisierungsschema anwendbar. Folglich fördert die Methodik weitere Forschungen zur Identifizierung der Zuverlässigkeit von CWE-Simulationen

Prediction of discretization error using the error transport equation

Since its conception, computational fluid dynamics (CFD) has had a role to play in both the industrial and the academic realm. Due to the availability of relatively cheap computer resources, CFD is now playing an increasingly critical role in the industry compared to experiments. It is also becoming increasingly important for the CFD analyst to have an in-depth understanding of the error inherently present in numeric and mathematical models. At a minimum, CFD simulation results should be accompanied by some analysis of the error including some type of grid convergence study and an estimation of the corresponding numerical uncertainty.;Error estimation is commonly done using a method known as Richardson Extrapolation (RE). While RE does produce good error predictions, the requirements for appropriate application of RE are often cumbersome and even prohibitive. In order to achieve an accurate estimate of the discretization error using RE, solutions on at least three grids are required. To obtain satisfactory results, all of these solutions must be in the asymptotic regime, which often requires solutions on more than three grids to verify. Solutions of practical interest in the industry are often quite complex and require a large number of grid points. In this situation, it is not always desirable to produce solutions on three significantly different grids.;This study focuses on an approach to quantify the discretization error associated with numerical solutions by solving an error transport equation (ETE). The goal is to develop a method that can be used to adequately predict the discretization error using the numerical solution on only one grid/mesh. The primary problem associated with solving the ETE is the development of the error source term which is required for the solution of the problem. In this study, a novel approach is considered which involves fitting the numerical solution with a series of locally smooth curve fits and then blending them together with a weighted spline approach. The result is a continuously differentiable analytic expression that can be used to determine the error source term. Once the source term has been developed, the ETE can easily be solved using the same solver that is used to obtain the original numerical solution.;The new methodology is applied to increasingly complex problems to quantify the discretization error. The method is first validated with the simplistic 1-D and 2-D convection diffusion problem. For both cases the results were very promising. However, in order for this method to be of practical use in the industry, the method must be applicable to the Navier-Stokes equations which are used to solve complete flow fields. The method is extended to solution of the Navier-Stokes equations with increasing complexity. The obtained results indicate that there is much promise going forward with the newly developed source evaluation technique and the ETE