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Well-Balanced and Invariant Domain Preserving Schemes for Dispersive Shallow Water Flows
No full textAs urbanization encroaches more on flood prone regions and paved surfaces are ever expanding, more catastrophic flash floods occurring in urban environments are expected in the near future. These risks are compounded by global changes in the climate. Mathematics can help better predict and understand these situations through modeling and numerical simulations. The aim of this work is to discuss current mathematical and computational issues in modeling shallow water flows with applications in coastal hydraulics, large-scale oceanography and in-land flooding.
Our mathematical starting points are the systems of partial differential equations known as the (i) Saint-Venant shallow water equations and (ii) dispersive Serre���Green���Naghdi (SGN) equations. The goal of this work is to efficiently solve both mathematical models supplemented with external physical source terms for in-land flooding and large-scale coastal oceanography applications. In particular, the work focuses on introducing a novel technique for solving the Serre���Green���Naghdi equations. We introduce new analytical solutions of the SGN equations with topography that are used to verify the accuracy of numerical methods. Then, we propose a new relaxation technique for solving the SGN equations with topography effects that yields a hyperbolic formulation of the equations. This relaxation technique allows us to circumvent the dispersive time step restriction of the Serre Equations which is a major challenge when solving the equations. This method is then supplemented with a novel continuous finite element approximation that is second-order accurate in space, invariant domain preserving and well-balanced. The method is then verified with academic benchmarks and validated by comparison with laboratory experimental data
Evaluating Avoidance Behaviors as Maintenance Factors for PTSD in Everyday Life
Get PDFAvoidance is a key component of Post-Traumatic Stress Disorder (PTSD) in which individuals escape or distract themselves from perceived threats by becoming physically or psychologically distant from uncomfortable thoughts, feelings, or situations. Safety behaviors are a form of avoidance, where individuals engage in preventative behaviors to avoid threatening consequences. Behaviors such as these are believed to maintain aspects of PTSD symptomatology. While studies have shown that some individuals with PTSD engage in safety behaviors, little work has been done on examining how safety behaviors contribute to post-traumatic stress in everyday life. To understand how individuals with post-traumatic stress engage in safety behaviors, this study takes place in a naturalistic setting which offers insight into the everyday lives of those with PTSD symptoms in a nonclinical adult sample. Participants with trauma exposure and who have experienced avoidance symptoms in the past month will undergo a 14-day self-report period in which their safety behavior usage and feelings of post-traumatic stress will be collected at 3 time points throughout the week. It is hypothesized that higher levels of safety behaviors at baseline will predict greater PTSD symptom levels during the self-report period. It is also hypothesized that safety behavior usage will amplify the effect of daily stressors on PTSD symptoms. Understanding how safety behavior usage can maintain post-traumatic stress symptoms in naturalistic settings is essential for improving psychological assessments, treatment planning, and outcomes
Role of Hypervelocity Mach Numbers on Optical Distortion
No full textTo characterize optical distortion in a hypervelocity ground test facility, a study comparing effects at three hypersonic Mach numbers simulated at true flight conditions was conducted. A highly modifiable wedge model and a beam distortion imaging technique were designed and implemented in Texas A&M University���s Hypervelocity Expansion Tunnel. Additionally, optical diagnostics, such as high-speed schlieren, optical emission spectroscopy, and focused laser differential interferometry were conducted. A laminar 11-species gas computational fluid dynamics model was run over the geometry to determine the level of species excitation resulting from the stagnation region. A comparison of optical distortion, index of refraction spectra, and index of refraction gradient spectra at Mach 9, 12, and 15 was conducted. The results confirmed the laminar boundary layer and shock layer 15.5 cm aft of the nose for Mach 12 and 15, but the Mach 9 flow was transitional. Additionally, maximum beam distortion occurred at Mach 9 due to a higher density flow-field. These investigations led to recommendations for refining the beam distortion imaging in HXT and geometry changes to the model to study turbulence