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Ducts can be found in ventilation systems, cooling ducts and blade passages of turbines, centrifugal pumps and many other engineering installations. The properties of the flow in ducts can significantly affect the performance and efficiency of these installation areas. The majority of the flows in ducts and engineering applications are turbulent. The work presented in this thesis focuses on the analysis of turbulent flows inside square sectioned ducts and ducts with bends. The accuracy of three different high resolution high order schemes in the context of Implicit Large Eddy Simulation (ILES) is analysed. The influence of a low Mach limiting technique, Low Mach Number Treatment (LMNT) is also studied. The schemes employed are Monotonic Upwind Scheme for Scalar Conservation Laws (MUSCL) with a 2nd order Monotonized Central (MC) and 5th order limiter, and a 9th order Weighted Essential Non-Oscillatory (WENO) limiter. The first case studied is a duct of square cross section . In the absence of experimental data for the duct case, the data from a plain channel flow is used to shed light on the results. The flow analysis points out the generation of secondary motions created by the existence of surrounding walls. All schemes employed lead to a similarly developed turbulent flow that is used to provide the turbulent boundary profile for the following case. LMNT proves to significantly assist MUSCL 2nd and 5th, that use it, in providing a turbulent profile similar to that of WENO 9th that did not employ the technique but is inherently less dissipative. The second case under study is that of a square sectioned duct with a 90o bend. The simulation output is in good agreement both qualitatively and quantitatively with the experimental data available in the literature. The generation of secondary flows inside the bend is observed without flow separation. Although the turbulent flow entering the domain is almost the same for all cases, differences between the schemes are noticed especially after the middle of the bend. LMNT leads to an overprediction of turbulence after that area for both schemes employing it while WENO 9th without LMNT provides the most accurate results compared to those provided by the experiment. The results demonstrate applicability of ILES to strongly confined flows with secondary motions and shed light on cognitive properties of a wide range of state of the art schemes.

Implicit Large Eddy Simulation (ILES) with high-resolution and high-order computational modelling has been applied to flows with turbulent mixing and combustion. Due to the turbulent nature, mixing of fuel and air and the subsequent combustion still remain challenging for computational fluid dynamics. However, recently ILES, an advanced numerical approach in Large Eddy Simulation methods, has shown encouraging results in prediction of turbulent flows. In this thesis the governing equations for single phase compressible flow were solved with an ILES approach using a finite volume Godunov-type method without explicit modelling of the subgrid scales. Up to ninth-order limiters were used to achieve high order spatial accuracy. When simulating non chemical reactive flows, the mean flow of a fuel burner was compared with the experimental results and showed good agreement in regions of strong turbulence and recirculation. The one dimensional kinetic energy spectrum was also examined and an ideal k−5/ 3 decay of energy could be seen in a certain range, which increased with grid resolution and order of the limiter. The cut-off wavenumbers are larger than the estimated maximum wavenumbers on the grid, therefore, the numerical dissipation sufficiently accounted for the energy transportation between large and small eddies. The effect of density differences between fuel and air was investigated for a wide range of Atwood number. The mean flow showed that when fuel momentum fluxes are identical the flow structure and the velocity fields were unchanged by Atwood number except for near fuel jet regions. The results also show that the effects of Atwood number on the flow structure can be described with a mixing parameter. In combustion flows simulation, a non filtered Arrhenius model was applied for the chemical source term, which corresponds to the case of the large chemical time scale compared to the turbulent time scale. A methane and air shear flow simulation was performed and the methane reaction rate showed non zero values against all temperature ranges. Small reaction rates were observed in the low temperature range due to the lack of subgrid scale modelling of the chemical source term. Simulation was also performed with fast chemistry approach representing the case of the large turbulent time scale compared to the chemical time scale. The mean flow of burner flames were compared with experimental data and a fair agreement was observed.

The main scope of this PhD thesis is the analysis of unsteady laminar and transitional suddenly expanded flows. For this reason Implicit Large Eddy Simulation (ILES) approach was used in combination with high order, high resolution numerical methods. The numerical methods examined are a 2nd order Monotonic Upwind Scheme for Scalar Conservation Laws (MUSCL) with Van Leer limiter, a high order (3rd) interpolation and a 5th order Weighted Essentially Non-Oscillatory scheme (WENO). First the numerical data for three low (steady state) Reynolds numbers and for two unsteady ( in the form of primary frequencies) were compared to the experimental data and were found in good agreement. A grid convergence study was undertaken for two Reynolds numbers demonstrating grid convergence and justifying the selection of the grid. The three numerical methods were evaluated for two Reynolds numbers showing good agreement for Reynolds number 412 and discrepancies at Reynolds number 900 between MUSCL and WENO with the MUSCL demonstrating a very dissipative behavior. The physical behavior of the flow in a wide range of Reynolds numbers were examined. For this range the flow behavior changed from steady to unsteady laminar and finally exhibiting localized transition to turbulence. The behavior of the main recirculation areas was described and the vortex shedding that occur there and how this change with the Reynolds number. The flow was observed to change from an unsteady quasi three dimensional flow at Reynolds number 412 to an increased transitional state with three dimensional vortical structures at Reynolds number 550. Kinetic energy spectra were calculated for the aforementioned range of Reynolds numbers. The primary frequencies are increasing with Reynolds number as expected. The slopes that were calculated for the inertial subrange revealed a trend. As the Reynolds number is increasing the slopes are decreasing approaching the value given by Kolmogorov -5/3.

This thesis concerns the numerical simulation of dilute macromolecular solutions. Present work details the development of a novel mesoscale simulation method. The developed modeling approach is capable to describe both the macroscopic flow field of the carrier liquid and the micromechanical behaviour of the transported large molecules. In this modeling method, the concept of micromechanical structures is introduced in order to represent macromolecules. The motion of the considered mechanical structures is governed by forces arising from the motion of the bulk fluid phase and microscopic forces arising from stochastic Brownian motion of the solvent molecules. This document presents the motivation, the objectives and systematic steps of the model development. The work presents detailed discussion, verification and validation of the developed modeling method.

Effective understanding of gas flow is important to ensure efficient operation of gas neutralizer systems such as those used at the Joint European Torus (JET), which form part of invaluable heating systems for nuclear fusion experiments. Computational fluid dynamics modelling of the neutral gas flow in the JET neutraliser has been undertaken, motivated by the shortfall in neutralisation efficiency and apparent loss of gas target observed in the JET neutraliser system. This has presented a challenging modelling endeavour due to the interaction of beam, background plasma and rarefied neutral gas. Utilising the continuum flow approximation, the Navier-Stokes and Augmented Burnett equations have been implemented and applied in conjunction with secondorder slip boundary conditions to form a gas solver accurate within the continuum-transition regime. Simulations in the presence of the ionic beam and background neutraliser plasma encountered during tokamak heating operations have been achieved via the development of a coupled beamplasma- gas solver. The gas flow governing equations have been supplemented by a series of source/sink terms for mass/energy that describe the complex web of interactions between the neutraliser constituents. The developed solver has been validated against experimental data, both in the absence and presence of beam. The design of future gas neutraliser systems has also been considered, with variation of several model and geometry parameters in order to better understand the loss of neutralisation efficiency and how future systems might be optimised. The neutraliser design for the forthcoming International Thermonuclear Experimental Reactor (ITER) has also been evaluated.

Many environmental flows are turbulent flows. Depending on the physical aspects of the wind and the urban topology, turbulence might result into unfavourable or even dangerous conditions for the pedestrians. Turbulence can also play a very important role in the transport of toxic pollutants from accidental or intentional releases. Thus, it is vital to understand its complex characteristics so that its features are accurately predicted when computational methods are used. Real urban environment involving separation and reattachment regions provides an excellent testcase for investigating such complex flows. This thesis is focused on analysing the physics involved in flows around building models pertinent to environmental flows in urban areas and to evaluate the applicability of Implicit Large-Eddy Simulation in simulating the specific type of flows. For this purpose, a number of high resolution schemes in the context of Implicit Large-Eddy Simulation (each representing di erent degrees of spatial discretisation accuracy) was assessed. The evaluation of the schemes involved direct validation against experimental data as well as comparisons with DNS and LES data regarding flows within roughness element arrays in staggered arrangements. Initially, the flow within an uniform height cubical matrix was simulated. Four numerical schemes were tested in three di erent grid resolutions. The results were found in very good agreement with the Laser Doppler Anemometry data and they even exhibit DNS-like characteristics in specific locations of comparisons. Thus, it was concluded that high order spatial discretisation schemes allow the accurate representation of reality even in relatively coarse computational meshes. The second case under investigation involved flows within a more realistic representation of urban topology. Results obtained within an array of sixteen elements with five di erent heights reveal that although the roughness of the area is increased, the wind’s velocity profile above the obstacles shares almost the same slope as in the case of the array of the four cubical element. It is believed that this thesis has expanded the range of applications in the context of Implicit Large Eddy Simulation using high resolution schemes and contributed in persuading the scientific community for its potentials.

Efficient heat transfer technologies are essential for magnetically confined fusion reactors; this applies to both the current generation of experimental reactors as well as future power plants. A number of High Heat Flux devices have therefore been developed specifically for this application. One of the most promising candidates is the HyperVapotron, a water cooled device which relies on internal fins and boiling heat transfer to maximise the heat transfer capability. Over the past 30 years, numerous variations of the HyperVapotron have been built and tested at fusion research centres around the globe resulting in devices that can now sustain heat fluxes in the region of 20 – 30MW/m2 in steady state. Unfortunately, there have been few attempts to model or understand the internal heat transfer mechanisms responsible for this exceptional performance with the result that design improvements are traditionally sought experimentally which is both inefficient and costly. This thesis seeks to develop an engineering model of the HyperVapotron device using commercial Computational Fluid Dynamics software. To establish the most appropriate modelling choices, in-depth studies were performed examining the turbulence models (within the Reynolds Averaged Navier Stokes framework), near wall methods, grid resolution and boiling submodels. Validation of the models is accomplished via comparison with experimental results as well as high order Implicit Large Eddy Simulation methods. It is shown that single phase cavity flows and their related heat transfer characteristics (time-averaged) can be accurately captured if the SST k-omega turbulence model is employed using a fine nearwall grid throughout the cavity (e.g. y+ < 1 throughout). Separately, multiphase solutions with tuned wall boiling models also showed reasonable agreement with experimental data for vertical boiling tubes. As more complex multiphase HyperVapotron models were constructed, it became clear that there is an intrinsic incompatibility between the fine grids required for the single phase heat transfer predictions and the coarser grids plus wall functions required by the boiling model. Ultimately, the full 3D solution was based on the coarser grids as the fall off in accuracy in single phase heat transfer only becomes significant for HyperVapotron designs with deeper cavities. Since it is also shown here that deeper cavities are generally less efficient, these grid induced errors become less relevant if the primary objective is to find optimised performance.Comparing the CFD solutions with HyperVapotron experimental data suggests that a RANS-based, multiphase model is indeed capable of predicting performance over a wide range of geometries and boundary conditions. Whilst a definitive set of design improvements is not defined here, it is expected that the methodologies and tools developed will enable designers of future High Heat Flux devices to perform significant virtual prototyping before embarking on the more costly build and test programmes.

Understanding the motion of fluids is crucial for the development and analysis of new designs and processes in science and engineering. Unstructured meshes are used in this context since they allow the analysis of the behaviour of complicated geometries and configurations that characterise the designs of engineering structures today. The existing numerical methods developed for unstructured meshes suffer from poor computational efficiency, and their applicability is not universal for any type of unstructured meshes. High-resolution high-order accurate numerical methods are required for obtaining a reasonable guarantee of physically meaningful results and to be able to accurately resolve complicated flow phenomena that occur in a number of processes, such as resolving turbulent flows, for direct numerical simulation of Navier-Stokes equations, acoustics etc. The aim of this research project is to establish and implement universal, high-resolution, very high-order, non-oscillatory finite-volume methods for 3D unstructured meshes. A new class of linear and WENO schemes of very high-order of accuracy (5 th ) has been developed. The key element of this approach is a high-order reconstruction process that can be applied to any type of meshes. The linear schemes which are suited for problems with smooth solutions, employ a single reconstruction polynomial obtained from a close spatial proximity. In the WENO schemes the reconstruction polynomials, arising from different topological regions, are non-linearly combined to provide high-order of accuracy and shock capturing features. The performance of the developed schemes in terms of accuracy, non-oscillatory behaviour and flexibility to handle any type of 3D unstructured meshes has been assessed in a series of test problems. The linear and WENO schemes presented achieve very high-order of accuracy (5 th ). This is the first class of WENO schemes in the finite volume context that possess highorder of accuracy and robust non-oscillatory behaviour for any type of unstructured meshes. The schemes have been employed in a newly developed 3D unstructured solver (UCNS3D). UCNS3D utilises unstructured grids consisted of tetrahedrals, pyramids, prisms and hexahedral elements and has been parallelised using the MPI framework. The high parallel efficiency achieved enables the large scale computations required for the analysis of new designs and processes in science and engineering.

This thesis presents the motivation, objectives and reasoning behind the undertaken PhD to investigate the capability of compressible Implicit Large Eddy Simulation (ILES) in simulating wall-bounded inhomogeneous flows with particular interest in the near wall region and further presents the progress achieved to date. Investigation includes the assessment of current ILES methods to resolve inhomogeneous turbulence as well as compressible turbulent boundary layers and to improve on those models further. A channel flow is an excellent problem to use to investigate the properties of a SGS model near a wall. The presence of a solid boundary tends to alter the behaviour of the turbulent flow in a number of ways that need to be modeled by the SGS model in order to correctly represent the flow near the wall and most importantly the boundary layer. The presence of the wall inhibits the growth of the small scales, alters the exchange mechanisms between the resolved and unresolved scales and finally gives rise in the SGS near wall region to important Reynolds-stress producing events. A literature survey was carried out to identify other numerical investigations in simulating channel flow as well as data that could be used for validation purposes. The main parameters used to validate the level of resolution in simulating channel flow are identified and a number of tools are developed. The primary parameters extensively used to validate LES simulations of channel flow throughout the literature are mean flow velocity profiles, turbulent kinetic energy, dissipation and shear stress profiles, wall shear stress and friction velocities as well as energy spectra in the spanwise and streamwise homogeneous directions. Compressible viscous ILES of inhomogeneous anisotropic turbulence in an incompressible channel flow at wall normal grid resolutions of 68, 96 and 128 cells are carried out with grid clustering applied to the wall normal direction. Initial results conducted in the compressible regime show that in order to obtain satisfactory results, medium and fine grids are required whereas on coarser grids, some additional numerical method is required. Each reconstruction scheme introduces a numerical dissipation characteristic to itself that maybe regarded as a sort of turbulence model. Thus depending on the required dissipation, a suitable limiter can be chosen. The investigation then moves on to supersonic turbulent flow incorporating shockboundary layer interaction. Only the slope-limiters that prove to simulate the flow in the fully developed turbulent channel best are favoured and then also utilised in the subsequent compressible ramp simulations. The capabilities of modelling the shock boundary layer interaction, mean turbulent profiles and shockwave angle are investigated and compared against those obtained by DNS simulations. It is found that the grid at the inlet of the ramp plays a significant role, since it needs to be fine enough to maintain the turbulent in flow at an acceptable level before reaching the shock-boundary layer interaction zone. Further, very high-order numerical reconstructions were found to have difficulties in remaining stable in the high gradient regions of the flow when formulated in conservative form and therefore solutions were not possible to obtain. Nonetheless, lower order reconstruction methods run smoothly and the momentum profiles obtained, matched closely those obtained by DNS.

Many problems in solid dynamics involve moving boundaries, finite elastoplastic deformations, and strong non-linear waves. Continuum modelling of such events is difficult on account of these characteristics, and there exist a number of inadequacies in current numerical algorithms. Furthermore, a comprehensive understanding of certain underlying processes is yet to be achieved which places a limit on the derivation of engineering models to simulate these occurrences. Much needed atomistic studies, capable of revealing much about the governing physical processes, remain limited by current computational resources. This thesis is devoted to targeting these difficulties by proposing new continuum numerical schemes and a means of studying both micro- and macro-scale behaviours via a dynamic coupling of continuum mechanics and molecular dynamics theory. Eulerian shock-capturing schemes have advantages for modelling problems involving complex non-linear wave structures and large deformations in solid media. Various numerical methods now exist for solving hyperbolic conservation laws that have yet to be applied to solid dynamics. A three-dimensional finite-volume scheme on fixed grids is proposed for elastoplastic solids. The scheme is based upon the Godunov flux method and thus requires solution of the Riemann problem. Both exact and approximate solutions are proposed for the special case of non-linear elasticity. An implicit algorithm is developed to allow for resolving rate-dependent inelastic deformations. The methods are tested against exact solutions in one-dimension, and symmetrical polar solutions in two- and three-dimensions. To account for multiple immiscible materials it is necessary to include some means of tracking material boundaries within a numerical scheme. A moving grid scheme is a simple means of accommodating transient boundaries. Interface tracking based on the use of level set functions is an attractive alternative for problems with sliding interfaces since it allows discontinuous velocity profiles at the material boundaries whilst employing fixed grids. Both of these methods are explored in the current context. A series of one-dimensional testcases have been carried out that demonstrate the ability of the numerical schemes to accurately resolve complex boundary conditions between interacting free surfaces. Where singularities occur in a system comprising solid materials, atomistic studies are invaluable for achieving a fundamental insight into the governing physical processes. However where non-linear waves are generated, domain size proves to be a limiting factor in achieving solutions free from numerical artifacts. A domain decomposition multi-scale modelling strategy is developed that couples the Eulerian shock capturing scheme with a molecular dynamics solver. The method is demonstrated for one-dimensional testcases involving strong shear waves and multiple components. Attention is devoted to resolving transient wave propagation free from spurious wave reflections through investigation of the numerical parameters.

From molecules to living organisms and from atoms to planets a variety of physical phe- nomena operate at different temporal and spatial scales. Understanding the nature of those phenomena is crucial for advancing new technologies in many disciplines. In micro and nanofluidics as the operational dimensions are downsized to smaller scales the surface-to- volume ratio increases and the surface phenomena become dominant. Numerical modelling is the key for obtaining a better insight into the processes involved. The Achilles heel of fine grain microscopic numerical simulations is their computational cost. Simulating a multiscale phenomenon with an accurate microscopic description is extremely demand- ing computationally. On the contrary, simulations of multiscale phenomena based only on macroscopic descriptions cannot fully capture the physics of the multiscale systems. In order to confront this dilemma multiscale frameworks, called hybrid codes, have been de- veloped to couple the microscopic and macroscopic description of a system and to facilitate the exchange of information. The aim of this research project is to establish and implement a robust hybrid molecular- continuum method for micro- and nano-scale fluid flows. Towards that direction a hybrid multiscale method named as Point Wise Coupling (PWC) has been developed. PWC aims to circumvent the limitations of the existing hybrid continuum/atomistic approaches and deliver a modular and applicable methodology. In the PWC, the whole domain is covered with the macroscopic solver and the microscale model enters as a local refinement. Ad- ditionally, numerical techniques based on neural networks are employed to minimise the cost of the molecular solver and reduce the outcomes’ variability induced by the fluctuating nature of the atomistic data. Molecular studies have been performed (i) to obtain a better insight of the interfacial phenomena in the solid/liquid interfaces, and (ii) to study the parametrisation of the molec- ular models and mapping of atomistic information to hybrid frameworks. Specifically, the impact of parameters, such as surface roughness and stiffness, to slip process is studied. PWC framework has been employed to study a number of fundamental test cases in- cluding Poiseuille flow of polymeric fluids, isothermal slip Couette flow and slip Couette flow with heat transfer. Attention is drawn to the boundary condition transfer from the continuum solver to the atomistic description. In the performed hybrid studies the effects of the numerical optimisation techniques (linear interpolation, neural networks) to simu- lations’ accuracy, stability and efficiency are studied. The outcomes of the simulations suggest that the neural networks scheme enhance the simulation’s efficiency by minimising the number of atomistic simulations and at the same time act as a smoothing operator for reducing the oscillations’ strength of the atomistic outputs.

The topic of this PhD is to investigate materials interfaces under the application of com-pressive forces and dynamic friction. Friction studies are important in applications for high-speed machining and ballistic penetration modelling, two areas where it is important to understand the behaviour of rapidly moving interfaces. Gaining insight into the velocity dependence of the effective tangential force, and its time-evolution, under various external loads is also of particular interest. It is important to understand on an atomic and/or molec-ular level the fundamentals of tribological processes. Some of the processes investigated in this thesis include plastic deformation due to high compression, the response of materials when sliding occurs in terms of temperature variation across the interface and its relation-ship with atomic diffusion. Moreover, the materials dependence on operating conditions of temperature, loading and dynamic friction are factors that ultimately determine the design of tribological systems. In the last few years it has been shown that materials properties depend on the size, as smaller specimens are relatively stronger than larger ones. This thesis is aiming to em-ploy state of the art numerical and theoretical methods, which are vital to give a significant insight and understanding of the fundamental issues concerning dynamic friction of tribo-logical processes at the atomic scale. The mechanical behaviour is investigated in detail to reveal an accurate theoretical description of the frictional force at metallic surfaces. Special consideration is taken into account for the mechanism that causes dissipation in the form of heat. The strong deformation when materials undergo dynamic friction causes energy to dissipate away from the interface at a high rate. Additionally, investigation of the plastic deformation and its variation under conditions prevalent at high speed sliding is carried out. Knowledge of the yield point under these conditions is important to obtain accurate constitutive models for the shear stresses. In-vestigating how the material strength varies under sliding friction and obtaining accurate evaluation of the stresses involved has proved difficult and time consuming. This is primar¬ily attributed to the fact that experiments are difficult to conduct and expensive facilities are required. This thesis focuses on aspects of this complex process with the aid of molecular dynamic simulations.

Noise is an environmental concern and due to the increasing interest in helicopters as an alternative inter-city transportation, research for more environment friendly helicopters is continuously growing. Building on this demand, this study aims at finding an efficient and accurate noise prediction tool for rotating sources. This study therefore investigates the modelling of noise from rotating sources such as helicopter rotors by addressing noise propagation in both subsonic and transonic/ supersonic regimes. The aim of this research is to explore the field of aeroacoustics prediction for rotor generated noise and to develop a noise prediction tool for sources moving in subsonic or supersonic flow regimes. The aeroacoustics predictions presented have been obtained using a hybrid approach. With such an approach the near field noise generation process is simulated by means of an aerodynamics prediction tool while the noise propagation to the near field is computed by mean of the Ffowcs Williams-Hawkings equation in time domain. For the near-field aerodynamic calculations di erent CFD tools have been exploited. More precisely, three test cases have been analysed. For the first test case of 2D aerofoil-vortex interaction, reproducing the experimental campaign of Lee et al., the near-field is computed via the commercial software Fluent. The unsteady implicit Euler solver with second order discretisation both in space and in time is exploited. This uses the ROE FDS scheme for the fluxes calculation. The same solver is used in the near-field simulations of the third test case, where the analysis of a non-lifting hovering rotor is carried out in delocalised conditions, reproducing the experiments of Purcell on the UH1H model rotor. The second test case analysed is based on the HELISHAPE experimental campaign for the ONERA model rotor in BVI conditions. Two comprehensive codes, from Agusta-Westland and Roma Tre, are used to simulate the complex aeromechanics of the rotor in low speed descent. The noise propagation phase has been performed via the new noise prediction tool developed during this study, named HelicA (for Helic-opter A-coustics). This tool is based on the Emission Surface formulation and exploits a novel root finder and Emission Surface construction algorithms. It can use control surfaces which are in subsonic or transonic/supersonic conditions. Verification and validation processes have been performed on the noise prediction tool before using this code in the aforementioned test cases. These processes are based on the comparison of the tool’s predictions with available analytical and numerical results. The verification and validation cases include sources moving at Mach numbers ranging from MT = 0 to MT > 1. The noise prediction tool is applied to the three aforementioned test cases and the results are in very good agreement with the measurements even for the strong shock delocalisation cases.

With the optimisation of fixed aerodynamic shapes reaching its limits, the active flow control concept increasingly attracts attention of both academia and industry. Adaptive wing technology, and shape morphing airfoils in particular, represents a promising way forward. The aerodynamic performance of the morphing profiles is an important issue affecting the overall aerodynamic performance of an adaptive wing. A new concept of active flow, the Active Camber concept has been investigated. The actuator is integrated into the aerofoil and aerofoil morphing is realized via camber deformation. In order to identify the most aerodynamically efficient designs, an optimisation study has been performed using high resolution methods in conjunction with a two equation eddy viscosity model. Several different types of previously proposed compressible filters, including monotone upstream-centered schemes for conservation laws (MUSCL) and weighted essential non-oscillatory (WENO) filters, are incorporated and investigated in the present research. The newly developed CFD solver is validated and the effect that high resolution methods have on turbulent flow simulations is highlighted. The outermost goal is the development of a robust high resolution CFD method that will efficiently and accurately simulate various phenomena, such as shock/boundary layer interaction, flow separation and turbulence and thus provide the numerical framework for analysis and aerodynamic aerofoil design. With respect to the latter a multi-objective integrated design system (MOBID) has been developed that incorporates the CFD solver and a state-of-the-art heuristic optimisation algorithm, along with an efficient parametrization technique and a fast and robust method of propagating geometric displacements. The methodologies in the MOBID system resulted in the identification of the design vectors that revealed aerodynamic performance gains over the datum aerofoil design. The Pareto front provided a clear picture of the achievable trade-offs between the competing objectives. Furthermore, the implementation of different numerical schemes led to significant differences in the optimised airfoil shape, thus highlighting the need for high-resolution methods in aerodynamic optimisation.

Molecular modelling of meso- and nanoscale dynamics is concerned with length and time scales that are in the transition zone from molecular to continuum models. Molecular simulation methods, in particular molecular dynamics (MD), only allow the simulation of relatively small nanoscale systems. Continuum methods, such as computational fluid dynamics (CFD), are applicable at macroscopic scales but cease to be valid for nanoscales. This thesis is focused on hybrid MD-CFD methods with geometrical decomposition that seek to bridge the gap between molecular and continuum modelling. The hybrid solution interface (HSI) establishes the coupling between the molecular and the continuum domain. In this work, different realisation approaches for the HSI, flux and state coupling, are discussed and compared. A detailed investigation on MD flux boundary conditions, the most crucial part of a flux based HSI, is carried out. Different schemes for the imposition of mass, momentum and energy fluxes through convective and viscous transport are presented: direct and indirect flux imposition for convective fluxes; the imposition of momentum fluxes through reflective walls, external forces and the reverse velocity scheme; and imposition of energy fluxes through external forces and an energy transfer scheme. Different combinations of these schemes are compared for standard flow situations. The momentum and energy transfer by an external force creates a relaxation zone at the MD boundary. The characteristics of this zone is investigated in detail and a theoretical model for the density profile has been derived. The reverse velocity scheme has been created as part of this work to avoid the problems encountered when using the external force for the momentum transfer. It is shown that indirect convective flux imposition in conjunction with the reverse velocity scheme gives the best results for the standard flow situations. The scheme is also tested for liquid flow past Carbon nanotubes.

High-order numerical methods have been considered and implemented in order to assess their applicability in a range of complex ows centering on shockinduced turbulent mixing. Speci cally, Weighted Essentially Non-Oscillatory (WENO) variable reconstruction schemes of fth and ninth order accuracy have been investigated within the context of a nite volume Godunov solver. In addition to this there have been further numerical developments to assess the HLLC Riemann solver and various quasi-conservative multi-component models in conjunction with the high-order methods. Understanding the physics of fundamental ow instabilities and turbulence is increasingly necessary to the development of a vast range of engineering applications with relation to uid dynamics. It is desirable to develop numerical methods that possess su cient accuracy to capture the detail of such ows while remaining robust and viable in terms of cost. The WENO schemes have been tested on a number of cases in comparison with more traditional second-order MUSCL schemes. These include two and three dimensional, single and multi mode Richtmyer-Meshkov instabilities with differing initial perturbations, a cube of homogeneous decaying turbulence and two hypersonic geometry cases were simulated. The results from this research were consistent. The higher-order methods provided measurably greater resolution of small scale uctuations. By conducting grid convergence studies it was seen that the e ect of the higher-order methods was comparable to the e ect of increasing the number of grid points. The cost analysis repeatedly showed that despite the additional cost of using a higher-order method they were much better value as they could resolve ow features on a signi cantly coarser grid. The high-order methods were not only validated for a range of ow problems but shown to o er great value for their additional cost; they could potentially help advance understanding and development in a wide range of elds much faster than is currently the case.

Most flows of practical importance are governed by viscous near-wall phenomena leading to separation and subsequent transition to a turbulent state. This type of problem currently poses one of the greatest challenges for computational methods because its characteristics covers a wide range of physical processes that often place contradictory requirements on the numerics employed. This thesis seeks to investigate the physics of complex, separated flows pertinent to aeronautical engineering and to assess the performance of variants of the Implicit Large-Eddy Simulation approach in predicting this type of problem realistically. For this purpose, different numerical solution strategies based on high-resolution methods, distinguished by their order of accuracy, are used in precursor simulations and one selected approach is applied to a fully three-dimensional wing flow. In order to isolate the development from laminar to turbulent flow after separation has occurred, the prototype Taylor-Green Vortex is considered. Here, the behaviour of the numerical schemes during the linear, non-linear and fully turbulent stages in the flow evolution is tested for different grid sizes. It is found that the resolution power and the likelihood of symmetry breaking is increasing with the order of accuracy of the numerical method. These two properties allow the flow to develop more realistically on coarse grids if higher order schemes are employed. In the next step, flow separation from a gently curved surface is included. The fundamental study of a statistically two-dimensional channel flow with hill-type constrictions demonstrates the basic applicability of ILES to problems featuring massive separation. Without specific wall-treatment, high-resolution methods can improve prediction of the detachment location when compared to classical Large-Eddy Simulations. Finally, an ILES simulation of three-dimensional flow over a swept wing geometry at moderate angle of incidence is presented. The results are in excellent agreement with experiment in the fully separated and turbulent region and they are more accurate than a classical hybrid RANS/LES approach, using a grid twice the size, over the majority of the wing. This outcome will probably settle the dispute that has erupted in the past over the applicability of ILES to complex, wall-bounded flows.

The study presented in this document is the result of three years of research into the complex world of Molecular Dynamics applied to biological cell membranes. The simulation of biological tissues involves not only an excellent knowledge of the numerical calculus and its related tools, but a profound comprehension of the biological and medical literature associated with the phenomenon. By the other hand, the use of high performance facilities is essential for the computation of the Molecular Dynamics models in order to obtain results in acceptable times, so the latest technological advances have played a decisive and important part in this eld of research. The presented obtained results about shock wave interaction with biological membranes, as well as the air ow through the alveolar surface, are part of a new line of research usually known as 'virtual experimental'. This name comes from the fact that any physical or chemical situation can be re-created into a computer system to calculate its propagation in time. The results of the interaction of shock waves with biological cell membranes have been particularly satisfactory and they have opened a new line of investigation into cancer research. A numerical proportional relation between the shock wave impulse and the value of lateral di usion (from 9.80 to 12.84 10 .7 cm2 s ), as well as the simulation of the transient provoked by the wave into a NPT ensemble are a successful achievement. Other computations of this type of interaction have been simulated into an NVE ensemble as well, however the obtained results for the lateral di usion, in the order of 10 .7 cm2 s , showed no trend regarding the shock wave and the transient e ect could not be simulated. On the other hand, the recreation of the air ow through the alveolar surface is an initial step into the solution of all the controversy surrounding this extremely complex system known as alveolar surface network. An alveolar membrane of around 7 nm has been successfully simulated in agreement with Scarpelli's experiments. This lipid-protein membrane model simulated can serve as a virtual experiment in order to solve the controversy about the alveolar surface. It points to the possibility of air ow through a stable two-layered DPPC phospholipid structure either from a numerical or physical and biological point of view and the existence of an alveolar membrane at the end of the bronchial tubes.

Numerical methods for the simulation of shock-induced turbulent mixing have been investigated, focussing on Implicit Large Eddy Simulation. Shock-induced turbulent mixing is of particular importance for many astrophysical phenomena, inertial confinement fusion, and mixing in supersonic combustion. These disciplines are particularly reliant on numerical simulation, as the extreme nature of the flow in question makes gathering accurate experimental data difficult or impossible. A detailed quantitative study of homogeneous decaying turbulence demonstrates that existing state of the art methods represent the growth of turbulent structures and the decay of turbulent kinetic energy to a reasonable degree of accuracy. However, a key observation is that the numerical methods are too dissipative at high wavenumbers (short wavelengths relative to the grid spacing). A theoretical analysis of the dissipation of kinetic energy in low Mach number flows shows that the leading order dissipation rate for Godunov-type schemes is proportional to the speed of sound and the velocity jump across the cell interface squared. This shows that the dissipation of Godunov-type schemes becomes large for low Mach flow features, hence impeding the development of fluid instabilities, and causing overly dissipative turbulent kinetic energy spectra. It is shown that this leading order term can be removed by locally modifying the reconstruction of the velocity components. As the modification is local, it allows the accurate simulation of mixed compressible/incompressible flows without changing the formulation of the governing equations. In principle, the modification is applicable to any finite volume compressible method which includes a reconstruction stage. Extensive numerical tests show great improvements in performance at low Mach compared to the standard scheme, significantly improving turbulent kinetic energy spectra, and giving the correct Mach squared scaling of pressure and density variations down to Mach 10−4. The proposed modification does not significantly affect the shock capturing ability of the numerical scheme. The modified numerical method is validated through simulations of compressible, deep, open cavity flow where excellent results are gained with minimal modelling effort. Simulations of single and multimode Richtmyer-Meshkov instability show that the modification gives equivalent results to the standard scheme at twice the grid resolution in each direction. This is equivalent to sixteen times decrease in computational time for a given quality of results. Finally, simulations of a shock-induced turbulent mixing experiment show excellent qualitative agreement with available experimental data.

This thesis concerns the numerical investigation of suddenly expanded flows featuring separation, instabilities and transition, in the context of Implicit Large Eddy Simulation (ILES). The study of separated flows through suddenly expanded geometries is a classic yet complex area of research. These types of flows feature instabilities which may lead to bifurcation. Non-linear bifurcation is of great importance when considering hydrodynamic stability and the mechanism of laminar to turbulent flow transition. A detailed numerical investigation of various high-resolution methods and their ability to correctly predict the flow through a suddenly expanded and contracted geometry demonstrates that the choice of the particular numerical method employed can lead to an incorrect solution of the flow. The key di erence between the various highresolution methods employed is in the calculation of the nonlinear wave-speed dependent term. It is shown that the nonlinearity of this term provides an asymmetric dissipation to the flow which triggers symmetry-breaking bifurcation in a fully symmetric computational set-up. High-resolution simulations of three-dimensional flow through a plane suddenly expanded channel at low Reynolds numbers show that this type of flow is characterised by a symmetric separation of the fluid which is nominally two-dimensional in the spanwise direction. Increasing the Reynolds number reveals a symmetry-breaking bifurcation of the fluid flow which becomes three-dimensional as Reynolds number is further increased. Simulations confirm that it is this threedimensional disturbance which leads to the onset of time-dependent flow characterised by the periodic shedding of vortices from the upstream recirculation zones. Preconditioning techniques which aim to alleviate sti ness in the calculation of the advective fluxes for low Reynolds number flows are shown to be unsuitable for flows featuring instabilities. The added dissipation to the flow causes the prediction of an incorrect stable solution or to an improper estimation of the size of the separation bubbles. Simulations of a synthetic jet issuing into quiescent air using various slope limiters manage to capture the flow physics relatively well. Limiters are used to avoid a scheme from being oscillatory and provide non-linear dissipation in the region of excessively large gradients. The various limiters di er with regards to the amount of dissipation they provide to the flow, hence the solution obtained is dependent on the limiter used.