An Ale Approach For The Numerical Simulation Of Insect Flight

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2014Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2014Bu çalışmada öncelikle büyük ölçekli (large-scale) hareketli yüzey problemlerinin tamamen birleşmiş (fully coupled) formda çözülmesi için kenar merkezli yapısal olmayan sonlu hacimler yöntemine dayalı Arbitrary Lagrangian-Eulerian (ALE) yöntemi geliştirilmiştir. Kenar merkezli sonlu hacim metoduna dayanan bu sayısal yöntemde hız vektör bileşenleri her bir elemanın yüzeylerinin orta noktasında tanımlanırken, basınç değerleri her bir elemanın merkezinde tanımlanmaktadır. Basınç ve hız değerlerinin mevcut şekilde düzenlenmesi kararlı bir sayısal şemaya yol açar ve böylece basınç noktalarının birbirleriyle etkileşmesi (pressure coupling) için ayrıca doğal olmayan bir değişikliğe ihtiyaç kalmaz. Süreklilik denklemi her bir eleman içerisinde tam olarak sağlanmakta ve bu süreklilik denklemlerinin toplamı hesaplama bölgesinin sınırlarında tanımlanan küresel süreklilik denklemini vermektedir. Geometrik korunum kanununun (GCL) ayrık biçimde (discrete formda) sağlanması için özel bir özen gösterilmiştir. Ağ deformasyonu her bir zaman adımında direkt olmayan radyal bazlı fonksiyon interpolasyonun çözülmesi ile elde edilmiş ve bu tekrar ağ oluşumunu gerektirmediğinden sayısal yöntemin performansını artırmıştır. Küçük zaman adımlı zamana bağlı akışların çözümü için projeksiyon metodunda olduğu gibi oluşan cebirsel denklemler üç ayrı matrise ayrıklaştırılmış ve bu matrislerin tersi önkoşullandırıcı olarak kullanılmıştır. Burada oluşan ayrık ölçekli Laplacian operatörünün tersi yerine iki adım HYPRE BoomerAMG önkoşullandırıcısı kullanılmıştır. Paralel önkoşullandırılmış iteratif yöntemlerin verimini artırmak için PETSc ve HYPRE kütüphanelerinden yararlanılmıştır. Hareketli ağlar üzerinde şu testler yapılmıştır: Azalan Taylor-Green Girdap akışı, kanal içindeki salınım hareketi yapan silindir etrafındaki akış, yere paralel salınım hareketi yapan küp içerisindeki küre etrafındaki akış.An arbitrary Lagrangian-Eulerian (ALE) approach has been developed in order to investigate the near wake structure of Drosophila flight. The numerical algorithm is based on side-centered finite volume method where the velocity vector components are defined at the mid-point of each cell face while the pressure is defined at the element centroid. The present arrangement of the primitive variables leads to a stable numerical scheme and it does not require any ad-hoc modifications in order to enhance pressure coupling. A special attention is also given to to satisfy the discrete global conservation law. An efficient and robust mesh-deformation algorithm based on the indirect radial basis function method is developed at each time level in order to enhance numerical robustness. For the algebraic solution of the resulting large-scale equations, a matrix factorization is introduced similar to that of the projection method for the whole coupled system and we use two-cycle of BoomerAMG solver for the scaled discrete Laplacian provided by the HYPRE library, which we access through the PETSc library. The present numerical algorithm is initially validated for the decaying Taylor-Green vortex flow, the flow past an oscillating circular cylinder in a channel and the flow induced by an oscillating sphere in a cubic cavity. Then the numerical method is applied to the numerical simulation of flow field around a pair of flapping Drosophila wings in hover flight. Finally, the numerical calculations with different wing kinematics are carried out to simulate the flow field around a pair of flapping Drosophila wings in hover.DoktoraPh

Immersed Boundary Methods in the Lattice Boltzmann Equation for Flow Simulation

In this dissertation, we explore direct-forcing immersed boundary methods (IBM) under the framework of the lattice Boltzmann method (LBM), which is called the direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM). First, we derive the direct-forcing formula based on the split-forcing lattice Boltzmann equation, which recovers the Navier-Stokes equation with second-order accuracy and enables us to develop a simple and accurate formula due to its kinetic nature. Then, we assess the various interface schemes under the derived direct-forcing formula. We consider not only diffuse interface schemes but also a sharp interface scheme. All tested schemes show a second-order overall accuracy. In the simulation of stationary complex boundary flows, we can observe that the sharper the interface scheme is, the more accurate the results are. The interface schemes are also applied to moving boundary problems. The sharp interface scheme shows better accuracy than the diffuse interface schemes but generates spurious oscillation in the boundary forcing terms due to the discontinuous change of nodes for the interpolation. In contrast, the diffuse interface schemes show smooth change in the boundary forcing terms but less accurate results because of discrete delta functions. Hence, the diffuse interface scheme with a corrected radius can be adopted to obtain both accurate and smooth results. Finally, a direct-forcing immersed boundary method (IBM) for the thermal lattice Boltzmann method (TLBM) is proposed to simulate non-isothermal flows. The direct-forcing IBM formulas for thermal equations are derived based on two TLBM models: a double-population model with a simplified thermal lattice Boltzmann equation (Model 1) and a hybrid model with an advection-diffusion equation of temperature (Model 2). The proposed methods are validated through natural convection problems with stationary and moving boundaries. In terms of accuracy, the results obtained from the IBMs based on both models are comparable and show a good agreement with those from other numerical methods. In contrast, the IBM based on Model 2 is more numerically efficient than the IBM based on Model 1. Overall, this study serves to establish the feasibility of the direct-forcing IB-LBM as a viable tool for computing various complex and/or moving boundary flow problems

Numerical investigation of the effects of free-surface flow past submerged bluff and streamlined bodies

PhDThe last decade has been marked by a continuous growth in computational power, which has allowed for elaborate modelling techniques like LES and DES applied at engineering scales which generally imply a Reynolds number in excess of 1×106. One field that has seen a rapid growth in use of numerical methods in design and performance analysis is the naval sector, especially in the design of submarines where the free-surface boundary plays an important role. This thesis is devoted to the study of free-surface flow past submerged bodies, with the objective of numerically studying free-surface flow past a submarine fairwater at periscope depth near actual operating conditions. This work is motivated by DSTL, who have reported that near periscope depth submarines exhibit an increased drag (private communication). In this work both LES and DES modelling approaches are also utilized, while the submerged body is accounted through the use of an immersed boundary method and the free-surface is through the use of a part moving mesh. The thesis is split in two main parts. The first part of the thesis focuses on low and moderate Reynolds number flow about a submerged cube (bluff body) for various submergence depths. Two configurations are examined one being that of a single cube in a uniform flow, while the other is that of a matrix of equally spaced cubes. Results show that for both cases a reduction in submergence depth causes the forces, the fluctuation in the forces and shedding frequencies to alter, while the level of interaction between vortices and free-surface to increase. The second part of this thesis focuses on the main study of free-surface flow past a submerged fairwater at a high and near operating Reynolds number. It is found that for both Reynolds numbers the flow behaviour shows little change, while the effects of reducing submergence depth results in the forces, the force variation and shedding frequency to increase. Surface waves are found to disperse by an angle of up to 40° for all submergence depth and are of the Kelvin wave kind. No direct interaction between vortical structures shed from the fairwater and free-surface are found, whilst the increases in forces acting on the fairwater are directly attributed due to wave motion.DSTL; Engineering and Physical Sciences Research Council (EPSRC)

Approximation anatomischer Strukturen und biomedizinischer Prozesse zur rechnergestützten Untersuchung der Hämodynamik in Aneurysmen

Arterien des Menschen können Aneurysmen aufweisen, deren Ruptur zu lebensbedrohenden inneren Blutungen wie Schlaganfällen führen kann. Ein Therapieansatz ist das Einsetzen von sogenannten Stents. Eine Ruptur oder der Einfluss eines Stents kann mit dem momentanen Stand der Technik nicht exakt vorhergesagt werden. Für eine optimale Behandlung von Patienten wäre dies allerdings eine wichtige Zusatzinformation für den behandelnden Arzt. Zur Bestimmung dieser Zusatzinformation sollen zukünftig Simulationen der Hämodynamik in pathologischen Arterien eingesetzt werden. In dieser Arbeit werden Strömungsgeschwindigkeiten in Arterien ohne beziehungsweise mit Einbringung von Einbauten wie Stents berechnet und die entstehenden Wandscherspannungen im Hinblick auf eine Rupturvorhersage untersucht. Weiterhin wird der Massentransfer zwischen Arterie und Aneurysma charakterisiert und eine Analyse des Thrombosierungsverhaltens unter Strömungseinfluss vorgenommen. Bei letztgenanntem Thema werden insbesondere der Verschluss von Aneurysmen durch Thromben, die Ortseindämmung der Thrombenbildung und das Verhalten von wandanhaftenden Thromben auch in Bezug auf eine Ablösung untersucht. Um hierfür geeignete Simulationen durchführen zu können, wird eine Analyse der biomedizinischen Grundlagen durchgeführt. Für die Untersuchung der komplexen Dynamik sind aus methodischer Sicht zwei grundlegende Aspekte zu bearbeiten: die geometrische und die funktionelle Approximation. Die funktionelle Approximation biomedizinischer Prozesse umfasst die Untersuchung der Blutströmung, des Transports von passiven Stoffen und der Thrombosierung. Hierfür werden entsprechende Modelle identifiziert, in entsprechende Lattice-Boltzmann-Verfahren umgewandelt, simuliert und untersucht. Durch die Erarbeitung geeigneter Konzepte für eine Umsetzung der hier beschriebenen Simulationen auf einzelnen oder mehreren, miteinander kommunizierenden Grafikprozessoren kann eine effiziente Simulation der gekoppelten Multi-Physik-Probleme mit Lattice-Boltzmann-Verfahren erreicht werden. Insgesamt stellt diese Vorgehensweise ein Novum dar und unterstreicht die Praktikabilität der Methode. Die geometrische Approximation anatomischer Strukturen wird in dieser Arbeit mit Level-Set-Darstellungen gelöst. Mit ihnen können vielfältige Problemstellungen im Umfeld der Simulation bearbeitet werden, dies umfasst beispielsweise die Konstruktion einer Simulationsdomäne aus unterschiedlichen Tomographiedaten und die Einbringung von Einbauten wie Stents in das Untersuchungsgebiet. Durch die Kombination mit der Lattice-Boltzmann-Methode können Vorteile gegenüber dem Stand der Technik erreicht werden, etwa bei der effizienten Berechnung der Wandscherspannungen. Eine Validierung der Strömungs- und Transportsimulationen wird mit hochaufgelöster Magnetresonanztomographie vorgenommen. Dazu wird ein Modell des Aufnahmevorgangs unter Einfluss von Radiofrequenz-Magnetfeldern und Gradienten erstellt und der Magnetisierungstransport sowie die Relaxation simuliert. Die bestimmten Abweichungen zwischen Simulation und Messung sind insgesamt gering. Für die Messexperimente werden erstmals 3D-Druckverfahren für die Konstruktion von physischen Modellen eingesetzt und deren Güte untersucht. Durch die Ergebnisse dieser Arbeit steht eine effiziente und umfassende Verarbeitungspipeline für Blutströmungs-, Transport- und Thrombosierungsprozesse für weitere Untersuchungen bereit. Sie kann ebenfalls leicht um neue Modelle erweitert werden. Die Simulation der Magnetresonanztomographie für Flussbildgebung ermöglicht ebenfalls zukünftige Anwendungen im Bereich der Sequenzentwicklung