This work details a multigrid-accelerated cut-cell Cartesian mesh methodology for the solution of a single partial differential equation set that describes incompressible as well as compressible flow. The latter includes sub-, trans- and supersonic flows. Cut-cell technology is developed which furnishes body-fitted meshes with an overlapping Cartesian mesh as starting point, and in a manner which is insensitive to surface definition inconsistencies. An edge-based vertex-centred finite volume method is employed for the purpose of spatial discretisation. Further, an alternative dual-mesh construction strategy is developed and the standard discretisation scheme suitably enhanced. Incompressibility is dealt with via a locally preconditioned artificial compressibility algorithm, and stabilisation is in all cases achieved with scalar-valued artificial dissipation. In transonic flows, shocks are captured via pressure switch-activated upwinding. The solution process is accelerated by the use of a full approximation scheme (FAS) multigrid method where coarse meshes are generated automatically via a volume agglomeration methodology. The developed modelling technology is validated by application to the solution of a number of benchmark problems. The standard discretisation as well as the alternative method are found to be equivalent in terms of both accuracy and computational cost. Finally, the multigrid implementation is shown to achieve decreases in CPU time of between a factor two to one order of magnitude. In the context of cut-cell Cartesian meshes, the above work has resulted in the following novel contributions: the development of an alternative vertex-centred discretisation method; the use of volume agglomerated multigrid solution technology and the use of a single equation set for both incompressible and compressible flows. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2007. / Mechanical and Aeronautical Engineering / unrestricted

The thesis explores the new expansions of eigenvalues for -£Gu =£f£lu in S with the Dirichlet boundary condition u=0 on $partial S$ by two conforming elements: the linear element $P_1$ and the bilinear element $Q_1$, and three non-conforming elements: the rotated bilinear element (denoted $Q_1^{rot}$), the extension of $Q_1^{rot}$ (denoted $EQ_1^{rot}$) and Wilson's element. The expansions indicate that $P_1$, $Q_1$ and $Q_1^{rot}$ provide the upper bounds of the eigenvalues, and $EQ_1^{rot}$ and Wilson's elements provide the lower bounds of the eigenvalues. Comparing the five finite elements, the $Q_1^{rot}$ element is more accurate. By the extrapolation, the superconvergence $O(h^4)$ can be obtained where $h$ is the boundary length of uniform squares. Numerical experiment are carried to verify the theoretical analysis made. (°Ñ·Ó¹q¤lÀÉp.4)

The advent of rapid manufacturing has enabled the realization of countless products that have heretofore been infeasible. From customized clear braces to jet fighter ducts and one-off dental implants, rapid manufacturing allows for increased design complexity and decreased manufacturing costs. The manufacturing capabilities of this process have evolved to the point that they have surpassed current design capabilities. Meso-scale lattice structures can now be built that contain more lattice struts than it is reasonable to efficiently define. This work has attempted to create a method for designing such lattice structures that is efficient enough to allow for the design of large or complex problems. The main hindrance to the design of complex meso-scale lattice problems is essentially the need to define the strut diameters. While it is obvious that a large design would contain more struts than can be specified by hand, designs also quickly surpass the current capabilities of computational optimization routines. To overcome this problem, a design method has been developed that uses a unit-cell library correlated to finite element analysis of the bounding geometry to tailor the structure to the anticipated loading conditions. The unit-cell library is a collection of base lattice primitives, or unit-cells, that have been specialized for certain applications. In this case, primitives have been created that perform best under the types of stress analyzed by finite element analysis. The effectiveness of this process has been demonstrated through several example problems. In all cases, the unit-cell library approach was able to create structures in less time than current methods. The resulting structures had structural performance slightly lower than similar models created through optimization methods, although the extent of this degradation was slight. The method developed in this work performs extremely well, and is able to create designs for even the most complex lattice structures. There is room for future development, however, in the streamlining of the design process and consideration of higher-order affects within unit-cells.

In this study we sought to compare eating disorder attitudes and behaviors, and proneness to an eating disorder (“ED proneness”), between gay men, lesbian women, and transgender and non-conforming (TGNC) adults. A further aim was to identify and compare risk and protective factors, and examine a mediational model based on the interpersonal theory of eating disorders (IPT-ED), whereby the association between interpersonal factors and ED proneness would be mediated by psychological constructs pertaining to the self and negative affect. Data was obtained from a larger national study of health risk and protective factors among sexual minority and gender diverse populations. The sample included 97 gay men, 82 lesbian women, and 138 TGNC adults. Participants completed the National College Health Assessment, Eating Disorders Screen for Primary Care, Patient Health Questionnaire Depression scale, Generalized Anxiety Disorder 7 scale, Self-Compassion Scale-Short Form, Negative Social Exchange subscale of the Multidimensional Health Profile, Interpersonal Needs Questionnaire, and Perceived Stigma Scale. There was a significant difference between groups in ED proneness, with lesbian women (66.7%) having a significantly higher percentage than gay men (47.6%). There was also a significant difference between groups in weight-based self-worth, with the lowest percentage in gay men (63%) and the highest percentage in lesbian women (82%), as well as dissatisfaction with eating patterns, with the highest percentage in TGNC adults (69.8%) and the lowest percentage in gay men (47.7%). There was a low percentage of inappropriate compensatory behaviors, with no significant difference between groups. Logistic regression analyses showed that the predictor variables of ED proneness were depression, perceived stigma, and self-compassion in gay men; depression in lesbian women; and self-compassion in the TGNC adults. Mediation analyses showed that thwarted belongingness (i.e., an unmet to belong) and perceived stigma had an indirect association with ED proneness that was mediated by self-compassion and depression (for perceived stigma alone) in gay men, depression in lesbian women, and self-compassion in TGNC adults. The interpersonal theory of eating disorders therefore extends to sexual minority and gender diverse populations; however, the results suggest a broadening of theoretical models and intervention programs to include the role of stigma and self-compassion.

Counselors sometimes use counseling assessments with transgender and gender nonconforming (TGNC) persons without understanding the experiences individuals have with those assessments. The American Counseling Association and the World Professional Association of Transgender Health identified that attention is needed with the practice of counseling assessments to ensure that helpful, ethical, and culturally sensitive services are available. The purpose of this study was to explore TGNC adults' experiences with counseling assessments. Gadamer's hermeneutics provided a framework to examine qualitative data as truth and validate the individuals' experiences with counseling assessments. Participants included 12 TGNC persons 18 years or older who had a counseling assessment provided by a mental health professional. Data were collected from questionnaires, a focus group, and individual interviews. Results from coding analysis revealed 6 themes: motivation, positive outcomes, barriers to participation, mental health professional, cultural sensitivity, and impact. Findings validated TGNC participants' experiences with counseling assessments and may be used to improve counseling assessment practices for TGNC persons.

This work presents a novel method to model immiscible incompressible fluids in a stable manner. Here, the immiscible behavior of the flow is described by the incompressible Navier-Stokes-Cahn-Hilliard model, which is based on a diffuse interface method. We introduce buoyancy effects in the model through the Boussinesq approximation in a consistent manner. A structure-preserving discretization is used to guarantee the linear stability of the discrete problem and to satisfy the incompressibility of the discrete solution at every point in space by construction. For the solution of the model, we developed the Portable Extensible Toolkit for Isogeometric Analysis with Multi-Field discretizations (PetIGA-MF), a high-performance framework that supports structure-preserving spaces. PetIGA-MF is built on top of PetIGA and the Portable Extensible Toolkit for Scientific Computation (PETSc), sharing all their user-friendly, performance, and flexibility features. Herein, we describe the implementation of our model in PetIGA-MF and the details of the numerical solution. With several numerical tests, we verify the convergence, scalability, and validity of our approach. We use highly-resolved numerical simulations to analyze the merging and rising of droplets. From these simulations, we detailed the energy exchanges in the system to evaluate quantitatively the quality of our simulations. The good agreement of our results when compared against theoretical descriptions of the merging, and the small errors found in the energy analysis, allow us to validate our approach. Additionally, we present the development of an unconditionally energy-stable generalized-alpha method for the Swift-Hohenberg model that offers control over the numerical dissipation. A pattern formation example demonstrates the energy-stability and convergence of our method.

This degree work investigates a Chinese ethnic identity in a Swedish social environment by means of translating national and cultural symbols, representing China and Sweden, into colors and materials within garments and accessories.Furthermore, this project demonstrates a transracial adoptee identity journey, through the act of conforming as a reaction to Swedish norms.To conduct the study, personal experiences of being a Chinese, Swedish adoptee have been applied to direct this work. An illustration of a timeline concerns the past and the present stages of a transracial adoptee identity and demonstrates the identity journey in chronological order, divided into five stages. This degree work generates new expressions within the social sustainability field in fashion by showcasing the absurdity to conform to Swedish norms. This work identifies how identity is formed by biological and social factors from a transracial adoptee perspective. This degree work demonstrates the complexity of transracial identity formation, through several layers, and criticizes Swedish norms through dress. It can spread awareness of the anxiety for transracial’s to fit into norms and recognition for those affected by it.

In the process of engineering design of structural shapes, the flat plate analysis results can be generalized to predict behaviors of complete structural shapes. In this case, the purpose of this project is to analyze a thin flat plate under conductive heat transfer and to simulate the temperature distribution, thermal stresses, total displacements, and buckling deformations. The current approach in these cases has been using the Finite Element Method (FEM), whose basis is the construction of a conforming mesh. In contrast, this project uses the mesh-free Scan Solve Method. This method eliminates the meshing limitation using a non-conforming mesh. I implemented this modeling process developing numerical algorithms and software tools to model thermally induced buckling. In addition, convergence analysis was achieved, and the results were compared with FEM. In conclusion, the results demonstrate that the method gives similar solutions to FEM in quality, but it is computationally less time consuming.

Nous présentons de nouveaux schémas numériques pour l'approximation de problèmes de diffusion hétérogène et anisotrope sur des maillages généraux. Sous des hypothèses correspondant aux cas industriels, nous montrons qu'un premier schéma, qui est centré sur les mailles, possède un petit stencil et converge dans le cas de tenseurs discontinus. La preuve de la convergence repose sur des propriétés de consistance des gradients discrets issus du schéma. Dans une seconde partie, nous proposons des méthodes de correction non linéaire du schéma initial pour obtenir le principe du maximum. L'efficacité de ces schémas est étudiée sur des tests numériques ayant fait l'objet de bancs d'essais d'une grande variété de schémas de volumes finis. Les comparaisons avec les schémas volumes finis classiques montrent l'apport de ces schémas en termes de précision. Nous montrons ainsi le bon comportement de ces schémas sur des maillages déformés, et le maintien de la précision des schémas non-linéaires, alors que les oscillations ont été supprimées / We present a new scheme for the discretization of heterogeneous anisotropic diffusion problems on general meshes. With light assumptions, we show that the algorithm can be written as a cell-centered scheme with a small stencil and that it is convergent for discontinuous tensors. The key point of the proof consists in showing both the strong and the weak consistency of the method. Besides, we study non-linear corrections to correct the FECC scheme, in order to satisfy the discrete maximum principle (DMP).The efficiency of the scheme is demonstrated through numerical tests of the 5th & 6th International Symposium on Finite Volumes for Complex Applications - FVCA 5 & 6. Moreover, the comparison with classical finite volume schemes emphasizes the precision of the method. We also show the good behaviour of the algorithm for nonconforming meshes. In addition, we give some numerical tests to check the existence for the non-linear FECC schemes

The aim of this thesis is to develop a flow solver that has the ability to obtain an accurate numerical solution fast and efficiently with minimum user intervention. In this study, a two-dimensional viscous, laminar, incompressible flow solver based on Least-Squares Spectral Element Method (LSSEM) is developed. The LSSEM flow solver can work on hp-type nonconforming grids and can perform p-type adaptive refinement. Several benchmark problems are solved in order to validate the solver and successful results are obtained. In particular, it is demonstrated that p-type adaptive refinement on hp-type non-conforming grids can be used to improve the quality of the solution. Moreover, it is found that mass conservation performance of LSSEM can be enhanced by using p-type adaptive refinement strategies while keeping computational costs reasonable.