Das unstetige Galerkinverfahren für Strömungen mit freier Oberfläche und im Grundwasserbereich in geophysikalischen Anwendungen

Free surface flows and subsurface flows appear in a broad range of geophysical applications and in many environmental settings situations arise which even require the coupling of free surface and subsurface flows. Many of these application scenarios are characterized by large domain sizes and long simulation times. Hence, they need considerable amounts of computational work to achieve accurate solutions and the use of efficient algorithms and high performance computing resources to obtain results within a reasonable time frame is mandatory. Discontinuous Galerkin methods are a class of numerical methods for solving differential equations that share characteristics with methods from the finite volume and finite element frameworks. They feature high approximation orders, offer a large degree of flexibility, and are well-suited for parallel computing. This thesis consists of eight articles and an extended summary that describe the application of discontinuous Galerkin methods to mathematical models including free surface and subsurface flow scenarios with a strong focus on computational aspects. It covers discretization and implementation aspects, the parallelization of the method, and discrete stability analysis of the coupled model.Für viele geophysikalische Anwendungen spielen Strömungen mit freier Oberfläche und im Grundwasserbereich oder sogar die Kopplung dieser beiden eine zentrale Rolle. Oftmals charakteristisch für diese Anwendungsszenarien sind große Rechengebiete und lange Simulationszeiten. Folglich ist das Berechnen akkurater Lösungen mit beträchtlichem Rechenaufwand verbunden und der Einsatz effizienter Lösungsverfahren sowie von Techniken des Hochleistungsrechnens obligatorisch, um Ergebnisse innerhalb eines annehmbaren Zeitrahmens zu erhalten. Unstetige Galerkinverfahren stellen eine Gruppe numerischer Verfahren zum Lösen von Differentialgleichungen dar, und kombinieren Eigenschaften von Methoden der Finiten Volumen- und Finiten Elementeverfahren. Sie ermöglichen hohe Approximationsordnungen, bieten einen hohen Grad an Flexibilität und sind für paralleles Rechnen gut geeignet. Diese Dissertation besteht aus acht Artikeln und einer erweiterten Zusammenfassung, in diesen die Anwendung unstetiger Galerkinverfahren auf mathematische Modelle inklusive solcher für Strömungen mit freier Oberfläche und im Grundwasserbereich beschrieben wird. Die behandelten Themen umfassen Diskretisierungs- und Implementierungsaspekte, die Parallelisierung der Methode sowie eine diskrete Stabilitätsanalyse des gekoppelten Modells

Numerical modelling of compressible turbulent premixed hydrogen flames

Turbulent combustion has a profound effect on the way we live our lives; homes and businesses predominantly rely on power generated by burning some form of fuel, and the vast majority of transport of passengers and cargo are driven by combustion. Fossil fuels remain readily available and relatively cheap, and so will continue to power the modern world for the foreseeable future. Combustion of fossil fuels produces emissions that detrimentally affect air quality, particularly in highly-populated cities, and are also widely believed to be contributing to global climate change. Consequently, increasing attention is being focused on alternative fuels, increased efficiency and reduced emissions. One alternative fuel is hydrogen, which introduces challenges in end-usage, storage and safety that are not encountered with more conventional fuels. Advances in computational power and software technology means that numerical simulation has a growing role in the development of combustors and safety evaluation. Despite these advances, many challenges remain; the broad range of time and length scales involved are coupled with complex thermodynamics and chemistry on top of turbulent fluid mechanics, which means that detailed simulations of even relatively-simple burners are still prohibitively expensive. Engineering turbulent flame models are required to reduce computational expense, and the challenge is to retain as much of the flow physics as possible. Furthermore, the choice of numerical approach has a significant effect on the quality of simulation, and different target applications place different demands on the numerical scheme. In the case of hydrogen explosion, the approach needs to be able to capture a range of physical behaviours including turbulence, low-speed deflagration, high-speed shock waves and potentially detonations. One such numerical approach that has enjoyed widespread success is finite volumes schemes based on the Godunov method. These methods perform well at all speeds, and have positive shock-capturing capability, but recent studies have demonstrated difficulties with numerical stability for more complex thermodynamics, specifically in the case of fully-conservative methods for multi-component fluids with varying thermodynamic properties. A recent development is the so-called double-flux method, which retains many of the positive properties of the fully-conservative approaches and does not suffer from the same numerical instabilities, but is quasi-conservative and involves additional computational expense. The present work consolidates the state-of-the-art in the literature, and considers two equation sets, based on mass fraction and volume fraction, respectively, along with fully-conservative and quasiconservative schemes. Comprehensive validation and evaluation of the different approaches is presented. It was found that both quasi-conservative approaches performed well, with a better conservative behaviour for the quasi-conservative volume fraction, but a better stability for the quasi-conservative mass fraction. Finally, the numerical tool developed is applied to turbulent combustion of premixed hydrogen in the context of the semi-confined experiments from the University of Sydney. The LES results showed an good overall agreement with the experimental data, and the critical parameters such as overpressure and flame speed where globally well captured, highlighting the large potential of LES for safety analysis

A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations

In this paper, we propose to improve the stabilized POD-ROM introduced by S. Rubino in [37] to deal with the numerical simulation of advection-dominated advection-diffusion-reaction equations. In particular, we introduce a stabilizing post-processing strategy that will be very useful when considering very low diffusion coefficients, i.e. in the strongly advection-dominated regime. This strategy is applied both for the offline phase, to produce the snapshots, and the reduced order method to simulate the new solutions. The new process of a posteriori stabilization is detailed in a general framework and applied to advection-diffusion-reaction problems. Numerical studies are performed to discuss the accuracy and performance of the new method in handling strongly advection-dominated cases

Large eddy simulation of partially premixed turbulent combustion

Imperial Users onl

On the numerical simulation of compressible flows

In this thesis, numerical tools to simulate compressible flows in a wide range of situations are presented. It is intended to represent a step forward in the scientific research of the numerical simulation of compressible flows, with special emphasis on turbulent flows with shock wave-boundary-layer and vortex interactions. From an academic point of view, this thesis represents years of study and research by the author. It is intended to reflect the knowledge and skills acquired throughout the years that at the end demonstrate the author’s capability of conducting a scientific research, from the beginning to the end, present valuable genuine results, and potentially explore the possibility of real world applications with tangible social and economic benefits. Some of the applications that can take advantage of this thesis are: marine and offshore engineering, combustion in engines or weather forecast, aerodynamics (automotive and aerospace industry), biomedical applications and many others. Nevertheless, the present work is framed in the field of compressible aerodynamics and gas combustion with a clear target: aerial transportation and engine technology. The presented tools allow for studies on sonic boom, drag, noise and emissions reduction by means of geometrical design and flow control techniques on subsonic, transonic and supersonic aerodynamic elements such as wings, airframes or engines. Results of such studies can derive in new and ecologically more respectful, quieter vehicles with less fuel consumption and structural weight reduction. We start discussing the motivation for this thesis in chapter one, which is placed into the upcoming second generation of supersonic aircraft that surely will be flying the skies in no more than 20 years. Then, compressible flows are defined and the equations of motion and their mathematical properties are presented. Navier Stokes equations arise from conservation laws, and the hyperbolic properties of the Euler equations will be used to develop numerical schemes. Chapter two is focused on the numerical simulation with Finite Volumes techniques of the compressible Navier-Stokes equations. Numerical schemes commonly found in the literature are presented, and a unique hybrid-scheme is developed that is able to accurately predict turbulent flows in all the compressible regimens (subsonic, transonic and supersonic). The scheme is applied on the flow around a NACA0012 airfoil at several Mach numbers, showing its ability to be used as a design tool in order to reduce drag or sonic boom, for example. At subsonic regimens, results show excellent agreement with reference data, which allowed the study of the same case at transonic conditions. We were able to observe the buffet phenomenon on the airfoil, which consists of shock-waves forming and disappearing, causing a dramatic loss of aerodynamic performance in a highly unsteady process. To perform a numerical simulation, however, boundary conditions are also required in addition to numerical schemes. A new set of boundary conditions is introduced in chapter three. They are developed for three-dimensional turbulent flows with or without shocks. They are tested in order to assess its suitability. Results show good performance for three-dimensional turbulent flows with additional advantages with respect traditional boundary conditions formulations. Unfortunately, compressible flows usually require high amounts of computational power to its simulation. High speeds and low viscosity result in very thin boundary layers and small turbulent structures. The grid required in order to capture this flow structures accurately often results in unfeasible simulations. This fact motivates the use of turbulent models and wall models in order to overcome this restriction. Turbulent models are discussed in chapter four. The Reynolds-Averaged Navier Stokes (RANS) approach is compared with Large-Eddy Simulation (LES) with and without wall modeling (WMLES). A transonic diffuser is simulated in order to evaluate its performance. Results showed the ability of RANS methods to capture shock-wave positions accurately, but failing in the detached part of the flow. LES, on the other hand, was not able to reproduce shock-waves positions accurately due to the lack of precision on the shock wave-boundary-layer interaction (SBLI). The use of a wall model, nevertheless, allowed to overcome this issue, resulting in an accurate method to capture shock-waves and also flow separation. More research on WMLES is encouraged for future studies on SBLIs, since they allow three-dimensional unsteady studies with feasible levels of computational requirements. With all these tools, we are able to solve at this point any problem concerned with the aerodynamic design of high-speed vehicles which were identified in previous paragraphs. Finally, multi-component flows are discussed in chapter five. Our hybrid scheme is upgraded to deal with multi-component gases and tested in several cases. We demonstrate that with a redefinition of the discontinuity sensor multi-components flows can be solved with low levels of diffusion while being stable in the presence of high scalar gradients. Because of the work of this thesis, a complete numerical approach to the numerical simulation of compressible turbulent multi-component flows with or without discontinuities in a wide range of Reynolds and Mach numbers is proposed and validated. Direct applications can be found in civil aviation (subsonic and supersonic) and engine operation.En aquesta tesis es presenten tècniques numèriques per a la simulació de compressibles en una gran varietat de situacions. L’objectiu és el de donar un pas endavant en la investigació científica de la simulació numèrica de fluids compressibles, amb especial èmfasi en fluxos turbulents amb interaccions entre ones de xoc, capa límit y vòrtex. Algunes de les aplicacions que es poden beneficiar d’aquesta investigació són: enginyeria marítima, combustió en motors, predicció meteorològica, aerodinàmica en la industria automotriu y aeronàutica, aplicacions biomèdiques y moltes altres. Tot i així, aquest treball s’emmarca en el camp de l’aerodinàmica compressible y la combustió de gasos amb un clar objectiu: el transport aeri i la tecnologia de motors. Les ferramentes presentades permeten l’estudi del sònic boom, resistència aerodinàmica, soroll y reducció d’emissions mitjançant el disseny geomètric i tècniques de control de flux en elements aerodinàmics tals com ales o motors en règims subsònics, transsònics i supersònics. Els resultats de tals estudis poden donar lloc a nous vehicles més ecològics, respectuosos amb el medi ambient, més silenciosos, amb menor peso estructural i menys consum de combustible.Postprint (published version

Large Eddy simulation of premixed combustion

Imperial Users onl

Numerical simulation of a non-reactive turbulent flow inside a cyclonic industrial boiler using LES and URANS

A numerical simulation of a non-reactive turbulent flow inside a cyclonic industrial CO boiler was investigated in order to understand the swirling formation, the fluid behavior in different locations inside the domain and the distribution of chemical species. As 80% of the energy matrix in Brazil is generated by combustion processes and government regulations about NOx emissions are becoming more restrict, enhancing combustion efficiency in a CO boiler with a turbulent swirling flow to reduce pollutant emissions has become an engineering research topic. Enhancing mixing processes through turbulent swirling flows might reduce thermal NOx formation. Computational fluid dynamics simulations were realized using the in-house MFSim code with the turbulent closure models LES, URANS Standard k − ", URANS Standard k − " Modified and URANS Realizable k − ". A theoretical basis about turbulence, LES and URANS closure models, mixing and swirling flows was provided. A state of art comprising different authors pointed out that some works with URANS Standard k − " demonstrated a premature solid-body rotation formation due to its eddy viscosity assumption and that swirling flows may reduce pollutant emissions by improving mixing of reactants and decreasing flame temperature. Validations concerning multi-component mixing flows and Immersed Boundary method were presented. From the results, LES and URANS Standard k − " presented similar velocity field results, capable of capturing the swirling formation. When analyzing three URANS closure models, a turbulent kinetic energy graph illustrated that it is relevant to observe the modeled part and the value obtained from velocity field fluctuations. The modified model presented low turbulent viscosity values and an LES-like behavior, with similar results to the standard model. The realizable model presented distant results comparing to the other models studied and there was no reverse flow in its swirling core. Adding different chemical species did not modify the velocity field and the highest mixing level was obtained in the most intense turbulent swirling region, close to the inlets. The data provided may assist in the comprehension of swirling formation, mixture processes inside a boiler and temperature control to reduce pollutant emissionsCAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorDissertação (Mestrado)Uma simulação numérica de um escoamento turbulento não reativo em uma caldeira industrial ciclônica de CO foi investigada a fim de se compreender a formação de um escoamento rotativo, o comportamento do fluido em diferentes locais dentro do domínio e a distribuição de espécies químicas. Como 80% da matriz energética no Brasil é gerada por processos de combustão e as regulamentações governamentais sobre as emissões de NOx estão se tornando mais restritas, o aumento da eficiência da combustão em uma caldeira de CO com escoamento turbulento ciclônico para reduzir as emissões de poluentes tornou-se um tema de pesquisa de engenharia. Melhorar os processos de mistura por meio de escoamentos turbulentos rotativos pode reduzir a formação térmica de NOx. Simulações de dinâmica dos fluidos computacional foram realizadas usando o código MFSim com os modelos de fechamento turbulento LES, URANS Standard k − ", URANS Standard k − " Modificado e URANS Realizable k − ". Foi fornecida uma base teórica sobre turbulência, modelos de fechamento LES e URANS, escoamentos com mistura e escoamentos rotativos. Um estado da arte compreendendo diferentes autores apontou que alguns trabalhos com URANS Standard k − " demonstraram uma formação de rotação de corpo sólido prematura devido à sua suposição de viscosidade turbulenta e que escoamentos rotativos podem reduzir as emissões de poluentes, melhorando a mistura de reagentes e diminuindo a temperatura da chama. Foram apresentadas as validações relativas aos escoamentos com mistura de multicomponentes e ao método da Fronteira Imersa. Dos resultados, LES e URANS Standard k − " apresentaram campos de velocidade semelhantes, capazes de capturar a formação de escoamento rotativo. Ao analisar três modelos de fechamento URANS, um gráfico de energia cinética turbulenta ilustrou que é relevante observar a parte modelada e o valor obtido a partir das flutuações do campo de velocidade. O modelo modificado apresentou baixos valores de viscosidade turbulenta e comportamento semelhante a LES, com resultados similares ao modelo Standard. O modelo realizável apresentou resultados distantes em comparação com os outros modelos estudados e não houve escoamento reverso em seu núcleo giratório. A adição de diferentes espécies químicas não modificou o campo de velocidade e o maior nível de mistura foi obtido na região de turbulência mais intensa, próxima às entradas. Os dados fornecidos podem auxiliar na compreensão da formação de escoamento rotativo, processos de mistura dentro de uma caldeira e controle de temperatura para reduzir as emissões de poluentes