5,607 research outputs found
A new numerical mesoscopic scale one-domain approach solver for free fluid/porous medium interaction
A new numerical continuum one-domain approach (ODA) solver is presented for the simulation of the transfer processes between a free fluid and a porous medium. The solver is developed in the \textit{mesoscopic} scale framework, where a continuous variation of the physical parameters of the porous medium (e.g., porosity and permeability) is assumed. The Navier--Stokes--Brinkman equations are solved along with the continuity equation, under the hypothesis of incompressible fluid. The porous medium is assumed to be fully saturated and can potentially be anisotropic. The domain is discretized with unstructured meshes allowing local refinements. A fractional time step procedure is applied, where one predictor and two corrector steps are solved within each time iteration. The predictor step is solved in the framework of a marching in space and time procedure, with some important numerical advantages. The two corrector steps require the solution of large linear systems, whose matrices are sparse, symmetric and positive definite, with -matrix property over Delaunay-meshes. A fast and efficient solution is obtained using a preconditioned conjugate gradient method. The discretization adopted for the two corrector steps can be regarded as a Two-Point-Flux-Approximation (TPFA) scheme, which, unlike the standard TPFA schemes, does not require the grid mesh to be K-orthogonal, (with {K the anisotropy tensor). As demonstrated with the provided test cases, the proposed scheme correctly retains the anisotropy effects within the porous medium. Furthermore, it overcomes the restrictions of existing mesoscopic scale one-domain approaches proposed in the literature
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Three-dimensional magnetic fields: from coils to reconnection
This thesis is a work divided into two parts on aspects of three-dimensional (3D) magnetic fields: (I) magnetic reconnection treated from a strictly 3D viewpoint and (II) the design of coils for producing the 3D magnetic fields of optimized stellarators.
In astrophysical settings, magnetic fields are generically 3D. 3D divergence-free fields have rich topological structures such as magnetic nulls and chaotic field line structures. Standard reconnection literature identifies magnetic nulls as locations of magnetic reconnection, and that intense currents will build up around them. This idea is explored with a key realization that by placing a vanishingly small sphere around the null, boundary conditions on field lines passing through the sphere may be sorted out. The main result here is (1) the dismissal of the notion that nulls are crucial places for magnetic reconnection and current accumulation, instead identifying separatrices of topological type on the boundaries of null-passing field lines to be crucial. Standard reconnection literature dismisses chaotic flows yet 3D fields generically have chaotic flows. An inherent property of chaotic flows is exponentiation. The main result here is (2) the identification of exponentiation as a natural mechanism for magnetic reconnection and that the associated current builds up linearly in time in contradiction to standard results requiring the formation of high-density current sheets.
The magnetic fields of optimized stellarators are intricate, producing complex 3D magnetic surfaces. These fields are conventionally generated by non-planar electromagnetic coils, though these coils are costly to manufacture, slow device assembly, and hinder stellarator maintenance. Part II of this thesis explores methods of stellarator coil simplification that do not involve modular coils. All of this work uses current potentials, which are stream functions of the current sheets that produce magnetic surfaces. We begin with a result found using analytic methods on current potentials that (1) there may be an inherent limitation in the ability of modular coils to produce fields at a distance. This result is not surprising, though further analysis is necessary to work out some complexities of the result.
Next, (2) a novel method to produce localized patches of current potential, representative of patches of current sheets, is developed and used to identify crucial locations of current placement for shaping magnetic surfaces. Most notably, these current sheet patches are able to produce much of the surface shaping while occupying a small fraction of the winding surface, resulting in good open-access stellarator coil configurations. Continuing the trend away from modular coils, (3) helical coils are optimized to support stellarator magnetic fields.
This work agrees with related work on the optimization of helical coils, finding them unsuitable to the precise production of equilibria generated by modular coils. To improve this result, we use coil sets of mixed-type: helical coils with windowpane coils or permanent magnets, to mitigate field error left behind by the helical coils. Finally, (4) the development of a generalized method to cut modular, helical, and windowpane coils out of current potentials and to identify the associated coil currents is developed and used in coil optimization
Modelling artificial ground freezing subjected to high velocity seepage
Artificial ground freezing (AGF) is a ground improvement technique for en- suring the safety of underground construction works in water-bearing soils. High velocity water transport in coarse-grain soils can prevent the ice wall formation in brine-based ground freezing methods. This can be overcome by using expendable refrigerants such as solid carbon dioxide and liquid nitro- gen, which provide much lower temperatures. Presented here is a model for analysis and design of ground freezing by expendable refrigerants under high velocity seepage conditions. Non-local mathematical formulations of heat transfer and water flow in soils are developed within the framework of the Peridynamics theory. Their computational implementation uses an adaptive multi-grid peridynamic approach to analyse large domains efficiently. The simulations are tested successfully against several benchmarks. The devel- oped model enables reliable analyses of the effects of main geological and technological parameters on the ice-wall delivery in the presence of ground- water flow
Temperature Reduction Technologies Meet Asphalt Pavement: Green and Sustainability
This Special Issue, "Temperature Reduction Technologies Meet Asphalt Pavement: Green and Sustainability", covers various subjects related to advanced temperature reduction technologies in bituminous materials. It can help civil engineers and material scientists better identify underlying views for sustainable pavement constructions
Numerical simulation of surfactant flooding with relative permeability estimation using inversion method
Surfactant flooding attracts significant interest in the hydrocarbon industry, with a definite
promise to improve oil recovery from depleting oil reserves. In this thesis, surfactant flooding
is the primary area of focus as it has significant potential for integration with other chemical
enhanced oil recovery techniques, including polymer, nanofluid, alkali, and foam. This
combined approach has the potential to reduce interfacial tension to ultralow levels, decrease
adsorption, and offer other benefits. However, due to the various mechanism, surfactant
flooding poses a more complex model for simulators by encountering numerical issues (e.g.,
the appearance of spurious oscillations, erratic pulses, and numerical instabilities), rendering
the methods ineffective. To address these challenges, the analytical modelling technique of
surfactant flooding was studied, leading to the development of a novel inversion method in the
MATLAB programming environment.
Numerical accuracy issues were discovered in 1D models that used typical cell sizes found in
well-scale models, leading to pulses in the oil bank and a dip in water saturation, particularly
for low levels of adsorption, highlighting the need for more refined models. Based on these
findings, we examined the surfactant flooding technique in 2D models to recover viscous oil
in short reservoir aspect ratios. Instabilities such as viscous fingering and gravity tongue were
observed on the flood fronts, and the magnitude of the viscous fingers was influenced by
vertical dispersion, resulting in errors in computed mobility values at the fronts. Interestingly,
introducing heterogeneity only minimally affected the spreading of the front and did not
significantly impact viscous fingering or numerical artifacts. To optimize the nonlinearity of
flow behaviour and degree of mobility control at the fronts, a homogenous model was
considered to develop the inversion method.
In summary, the developed inversion method accurately estimated the two-phase relative
permeability curves, which were validated using fractional flow theory. The precision of the
inverted curves was further improved using the optimization algorithm, demonstrating the
method's ability to predict outcomes closer to the observed values for 2D models with
instabilities. The obtained results are of significant value for core flood analysis, interpretation,
matching, and upscaling, providing insights into the potential of surfactant flooding for
enhanced oil recovery. Additionally, the use of the developed MATLAB Scripts promotes open
innovation and reproducibility, contributing to the benchmarking, analytical, and numerical
method development exercises for tutorials aimed at improving the overall understanding of
surfactant flooding
Enhancing the Structural Stability of α-phase Hybrid Perovskite Films through Defect Engineering Approaches under Ambient Conditions
This thesis investigates methods whereby perovskite solar cell power conversion efficiency and material stability
may be improved. Hybrid perovskites have gained increased attention for optoelectronic applications due to
favourable properties such as strong absorption, facile processing, and changeable band-gap. Despite excellent
improvements in power conversion efficiency of devices, perovskite films are unstable, degrading with relative
ease in the presence of moisture, oxygen, light, heat, and electric fields. The focus of this thesis is on ambient
atmosphere stability, concerned with the influence of moisture in particular on perovskite film fabrication,
degradation, and device functionality. In order to shed light on the impact of ambient atmosphere on perovskite
films, experiments are designed to investigate films during fabrication and degradation. The influences firstly of
stoichiometry during ambient fabrication, and then ionic substitution (with caesium and formadinium) upon
moisture-induced degradation are investigated. Finally, films and devices with a novel composition
incorporating Zn are fabricated under ambient conditions to investigate the effect of Zn addition on perovskite
film stability
On slope limiting and deep learning techniques for the numerical solution to convection-dominated convection-diffusion problems
As the first main topic, several slope-limiting techniques from the literature are presented, and various novel methods are proposed. These post-processing techniques aim to automatically detect regions where the discrete solution has unphysical values and approximate the solution locally by a lower degree polynomial. This thesis's first major contribution is that two novel methods can reduce the spurious oscillations significantly and better than the previously known methods while preserving the mass locally, as seen in two benchmark problems with two different diffusion coefficients.
The second focus is showing how to incorporate techniques from machine learning into the framework of classical finite element methods. Hence, another significant contribution of this thesis is the construction of a machine learning-based slope limiter. It is trained with data from a lower-order DG method from a particular problem and applied to a higher-order DG method for the same and a different problem. It reduces the oscillations significantly compared to the standard DG method but is slightly worse than the classical limiters.
The third main contribution is related to physics-informed neural networks (PINNs) to approximate the solution to the model problem. Various ways to incorporate the Dirichlet boundary data, several loss functionals that are novel in the context of PINNs, and variational PINNs are presented for convection-diffusion-reaction problems. They are tested and compared numerically. The novel loss functionals improve the error compared to the vanilla PINN approach. It is observed that the approximations are free of oscillations and can cope with interior layers but have problems capturing boundary layers
Acoustic Propagation Variation with Temperature Profile in Water Filled Steel Pipes at Pressure
Conventional pressure leak testing of buried pipelines compares measurements of pressure with pipe wall temperature. An alternative proposed method uses acoustic velocity measurements to replace pipe wall temperature measurements. Early experiments using this method identified anomalous results of rising acoustic velocities thought to be caused by air solution.
This research investigated the anomalous acoustic velocity measurements by evaluation of acoustic velocity variation with pressure, temperature and air solution. Quiescent air solution rate experiments were carried out in water filled pipes. Computer modelling of the air bubble shape variation with pipe diameter was found to agree with bubble and drop experiments over the pipe diameter range from 100 mm to 1000 mm. Bubbles were found to maintain constant width over a large volume range confirmed by experiments and modelling
Integrated Geophysical Analysis of Passive Continental Margins: Insights into the Crustal Structure of the Namibian Margin from Magnetotelluric, Gravity, and Seismic Data
Passive continental margin research amalgamates the investigation of many broad topics, such as the emergence of oceanic crust, lithospheric stress patterns and plume-lithosphere interaction, reservoir potential, methane cycle, and general global geodynamics. Central tasks in this field of research are geophysical investigations of the structure, composition, and dynamic of the passive margin crust and upper mantle. A key practice to improve geophysical models and their interpretation, is the integrated analysis of multiple data, or the integration of complementary models and data. In this thesis, I compare four different inversion results based on data from the Namibian passive continental margin. These are a) a single method MT inversion; b) constrained inversion of MT data, cross-gradient coupled with a fixed structural density model; c) cross-gradient coupled joint inversion of MT and satellite gravity data; d) constrained inversion of MT data, cross-gradient coupled with a fixed gradient velocity model. To bridge the formal analysis of geophysical models with geological interpretations, I define a link between the physical parameter models and geological units. Therefore, the results from the joint MT and gravity inversion (c) are correlated through a user-unbiased clustering analysis. This clustering analysis results in a distinct difference in the signature of the transitional crust south of- and along the supposed hot-spot track Walvis Ridge. I ascribe this contrast to an increase in magmatic activity above the volcanic center along Walvis Ridge. Furthermore, the analysis helps to clearly identify areas of interlayered massive, and weathered volcanic flows, which are usually only identified in reflection seismic studies as seaward dipping reflectors. Lastly, the clustering helps to differentiate two types of sediment cover. Namely, one of near-shore, thick, clastic sediments, and one of further offshore located, more biogenic, marine sediments
Data-driven deep-learning methods for the accelerated simulation of Eulerian fluid dynamics
Deep-learning (DL) methods for the fast inference of the temporal evolution of fluid-dynamics systems, based on the previous recognition of features underlying large sets of fluid-dynamics data, have been studied. Specifically, models based on convolution neural networks (CNNs) and graph neural networks (GNNs) were proposed and discussed.
A U-Net, a popular fully-convolutional architecture, was trained to infer wave dynamics on liquid surfaces surrounded by walls, given as input the system state at previous time-points. A term for penalising the error of the spatial derivatives was added to the loss function, which resulted in a suppression of spurious oscillations and a more accurate location and length of the
predicted wavefronts. This model proved to accurately generalise to complex wall geometries not seen during training.
As opposed to the image data-structures processed by CNNs, graphs offer higher freedom on how data is organised and processed. This motivated the use of graphs to represent the state of fluid-dynamic systems discretised by unstructured sets of nodes, and GNNs to process such graphs. Graphs have enabled more accurate representations of curvilinear geometries and higher resolution placement exclusively in areas where physics is more challenging to resolve. Two novel
GNN architectures were designed for fluid-dynamics inference: the MuS-GNN, a multi-scale GNN, and the REMuS-GNN, a rotation-equivariant multi-scale GNN. Both architectures work by repeatedly passing messages from each node to its nearest nodes in the graph. Additionally, lower-resolutions graphs, with a reduced number of nodes, are defined from the original graph,
and messages are also passed from finer to coarser graphs and vice-versa. The low-resolution graphs allowed for efficiently capturing physics encompassing a range of lengthscales.
Advection and fluid flow, modelled by the incompressible Navier-Stokes equations, were the two types of problems used to assess the proposed GNNs. Whereas a single-scale GNN was sufficient to achieve high generalisation accuracy in advection simulations, flow simulation highly benefited from an increasing number of low-resolution graphs. The generalisation and long-term accuracy of these simulations were further improved by the REMuS-GNN architecture, which
processes the system state independently of the orientation of the coordinate system thanks to a rotation-invariant representation and carefully designed components. To the best of the author’s knowledge, the REMuS-GNN architecture was the first rotation-equivariant and multi-scale GNN.
The simulations were accelerated between one (in a CPU) and three (in a GPU) orders of magnitude with respect to a CPU-based numerical solver. Additionally, the parallelisation of multi-scale GNNs resulted in a close-to-linear speedup with the number of CPU cores or GPUs.Open Acces
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