Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This document discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this document the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant.

We have surveyed 84 Class 0, Class I, and flat-spectrum protostars in mid-infrared [Si II], [Fe II], and [S I] line emission, and 11 of these in far-infrared [O I] emission. We use the results to derive their mass. outflow rates, (M) over dot(w). Thereby we observe a strong correlation of (M) over dot(w) with bolometric luminosity, and with the inferred mass accretion rates of the central objects, (M) over dot(a), which continues through the Class 0 range the trend observed in Class II young stellar objects. Along this trend from large to small mass. flow rates, the different classes of young stellar objects lie in the sequence Class 0-Class I/flat-spectrum-Class II, indicating that the trend is an evolutionary sequence in which (M) over dot(a) and (M) over dot(w) decrease together with increasing age, while maintaining rough proportionality. The survey results include two that. are key tests of magnetocentrifugal outflow-acceleration mechanisms: the distribution of the outflow/accretion branching ratio b = (M) over dot(w)/(M) over dot(a), and limits on the distribution of outflow speeds. Neither rules out any of the three leading outflow-acceleration, angular-momentum-ejection mechanisms, but they provide some evidence that disk winds and accretion-powered stellar winds (APSWs) operate in many protostars. An upper edge observed in the branching-ratio distribution is consistent with the upper bound of b = 0.6 found in models of APSWs, and a large fraction (31%) of the sample have a. branching ratio sufficiently small that only disk winds, launched on scales as large as several au, have been demonstrated to account for them.

Supernovae (SNe) are energetic explosions that signal the end of a star's life. These events and the supernova remnants (SNRs) they leave behind play a central role in stellar feedback by adding energy and momentum and metals to the interstellar medium (ISM). Emission associated with these feedback processes, especially atomic and molecular line emission as well as thermal and nonthermal continuum emission is known to be enhanced in regions of high density, such as dense circumstellar matter (CSM) around SNe and molecular clouds (MCs). In this thesis, I begin with a brief overview of the physics of SN shocks in Chapter 1, focusing on a foundation for studying pan-chromatic signatures of interactions between SNe and dense environments. In Chapter 2, I examine an unusual SN with signatures of CSM interaction in the form of narrow lines of hydrogen (Type IIn) and thermal continuum emission. This SN appears to belong to a class of Type Ia SNe that shares spectroscopic features with Type IIn SNe. I discuss the difficulties of decomposing spectra in a regime where interaction occurs between SN ejecta and CSM, potentially confusing the underlying SN type. This is followed by a discussion of rebrightening that occurred at late-time in 𝐵 and 𝑉 band photometry of this SN, possibly associated with clumpy or dense CSM at large distances from the progenitor. In Chapter 3, I examine synchrotron emission from Cassiopeia A, observed in the 𝐾ₛ band over multiple epochs. The synchrotron emission is generally diffuse over the remnant, but there is one location in the southwest portion of the remnant where it appears to be enhanced and entrained as knots of emission in the SNR ejecta. I evaluate whether the 𝐾ₛ band knots are dominated by synchrotron emission by comparing them to other infrared and radio imaging that is known to be dominated by synchrotron emission. Concluding that they are likely synchrotron-emitting knots, I measure the magnetic field strength and electron density required for their evolution over the ~ 10 yr baseline they were observed and find 𝐵 ≈ 1.3-5.8 mG and 𝑛ₑ≈ 1,000-15,000 cm⁻³. The magnetic field strengths appear enhanced beyond values required by the adiabatic strong shock limit, arguing in favor of other forms of magnetic field amplification in the shock. In Chapter 4, I again discuss Cassiopeia A and interaction between the remnant and nearby MCs as seen at mid-infrared and millimeter wavelengths. I report detection of a SNR-MC interaction and analyze its signatures in broadened molecular lines. I extend this analysis in Chapter 5 to a large survey for SNR-MC interactions in the ¹²CO 𝐽=2-1 line. Although broadened ¹²CO 𝐽=2-1 line emission should be detectable toward virtually all SNR-MC interactions, I find relatively few examples; therefore, the number of interactions is low. This result favors mechanisms other than supernova feedback as the basic trigger for star formation. In addition, I find no significant association between TeV gamma-ray sources and MC interactions, contrary to predictions that SNR-MC interfaces are the primary venues for cosmic ray acceleration. I end this dissertation in Chapter 6 with a brief summary of my results and two extensions of this work: examining the late-time radio light curves of CSM-interacting SNe for signatures of radio synchrotron emission and dense or clumpy CSM at large distances from the progenitor and re-observing SNR-MC interactions in ¹²CO 𝐽=3-2 in order to verify the presence of shock-heated molecular gas and perform a census on the densities and temperatures of post-shock molecular gas.

Student Number : 9803381J - MSc Dissertation - Faculty of Engineering and the Built Environment / Although pulsed power has been used in many parts of the world over the last few decades to initiate high-voltage discharges through rock, no systematic test work on South African ore bodies and related rock types has been done so far. As part of CSIR Miningtek’s integrated approach of combining underground comminution with a novel Tore© hydrotransport system, which has been shown to operate well with coarse particles up to 10 mm, various rock types were fragmented in single discharge mode under laboratory conditions. The work was conducted at the University of the Witwatersrand’s high-voltage laboratory with a custom-designed test rig. The rig configuration was based on a critical review and analysis of the literature and on assessments of existing test facilities elsewhere. Core samples with diameters ranging from 16 to 48 mm were cut from test specimens with thicknesses ranging from 8 to 48 mm. Rock types included Ventersdorp Contact Reef, Carbon Leader, Elsburg Formation, UG2 and Merensky, as well as pure quartz, shales, lava and dykes. A six-stage Marx generator provided a voltage rise time of 2 000 kV/μs to create a discharge through the rock, in preference to a discharge through the surrounding water, which acts as an insulator at ramp-up times faster than 0,5 μs. High-speed photography, and an analysis of the voltage and current signals for various rock types and for water alone, were used to quantify the potential benefits of rock breaking by electric discharge. It was found that some Kimberlite specimens and mineralised gold-bearing reefs were much easier to fragment than hanging wall or footwall material. Merensky reef appeared to be more susceptible than the less brittle UG2 material. A correlation was derived between the dynamic resistivity of various rock types, measured at 16 MHz excitation frequency, and the electrical breakdown strength at which discharge took place. The fragments created had a more cubical shape than would be created by conventional impact crushing. However, the high voltage requirements of about 30 to 35 kV per millimetre of rock thickness would necessitate not only efficient mechanical and electrical contact between the electrodes and the rock, but also considerable safety features for underground installations. The clearly identified, preferential fracturing of reef rock types, compared with the hanging or footwall materials, suggests that the greater benefit of electric rock breaking may lie in primary rock breaking as a mining method, rather than in secondary comminution of broken rock to enable hydraulic transportation by pipeline to surface.

Thesis. 1975. M.S.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / Bibliography: leaves 97-98. / M.S.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Michael E. McClurken. / Ph.D.

Xie Chunjing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 65-71). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Stability of Shock Waves in Viscous Conservation Laws --- p.10 / Chapter 1.1 --- Cauchy Problem for Scalar Viscous Conservation Laws and Viscous Shock Profiles --- p.10 / Chapter 1.2 --- Stability of Shock Waves by Energy Method --- p.15 / Chapter 1.3 --- Nonlinear Stability of Shock Waves by Spectrum Anal- ysis --- p.20 / Chapter 1.4 --- L1 Stability of Shock Waves in Scalar Viscous Con- servation Laws --- p.26 / Chapter 2 --- Propagation of a Viscous Shock in Bounded Domain and Half Space --- p.35 / Chapter 2.1 --- Slow Motion of a Viscous Shock in Bounded Domain --- p.36 / Chapter 2.1.1 --- Steady Problem and Projection Method --- p.36 / Chapter 2.1.2 --- Projection Method for Time-Dependent Prob- lem --- p.40 / Chapter 2.1.3 --- Super-Sensitivity of Boundary Conditions --- p.43 / Chapter 2.1.4 --- WKB Transformation Method --- p.45 / Chapter 2.2 --- Propagation of a Stationary Shock in Half Space --- p.50 / Chapter 2.2.1 --- Asymptotic Analysis --- p.50 / Chapter 2.2.2 --- Pointwise Estimate --- p.51 / Chapter 3 --- Nonlinear Stability of Viscous Transonic Flow Through a Nozzle --- p.58 / Chapter 3.1 --- Matched Asymptotic Analysis --- p.58 / Bibliography --- p.65

Zhang Hedan. / Thesis submitted in: September 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 78-81). / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Convex Scalar Conservation Laws --- p.9 / Chapter 2.1 --- Cauchy Problems and Weak Solutions --- p.9 / Chapter 2.2 --- Rankine-Hugoniot Condition --- p.11 / Chapter 2.3 --- Entropy Condition --- p.13 / Chapter 2.4 --- Uniqueness of Weak Solution --- p.15 / Chapter 2.5 --- Riemann Problems --- p.17 / Chapter 3 --- General Scalar Conservation Laws --- p.21 / Chapter 3.1 --- Entropy-Entropy Flux Pairs --- p.21 / Chapter 3.2 --- Admissibility Conditions --- p.22 / Chapter 3.3 --- Kruzkov Theory --- p.23 / Chapter 4 --- Elementary waves and Riemann Problems for Nonconvex Scalar Conservation Laws --- p.35 / Chapter 4.1 --- Basic Facts --- p.35 / Chapter 4.2 --- Riemann Solutions --- p.36 / Chapter 5 --- Asymptotic Behavior --- p.46 / Chapter 5.1 --- Periodic Asymptotic Behavior --- p.46 / Chapter 5.2 --- Asymptotic Behavior of Convex Conservation Law --- p.49 / Chapter 5.3 --- Asymptotic Behavior of Non-convex case --- p.52 / Chapter 5.3.1 --- L∞ Behavior --- p.53 / Chapter 5.3.2 --- Wave-Interactions and Asymptotic Behavior Toward Shock Waves --- p.55 / Bibliography --- p.78

This thesis presents a combined numerical and experimental study on the response of kidney cells to shock waves. The motivation was to develop a mechanistic model of cell deformation in order to improve the clinical use of shock waves, by either enhancing their therapeutic action against target cells or minimising their impact on healthy cells. An ultra-high speed camera was used to visualise individual cells, embedded in tissue-mimicking gel, in order to measure their deformation when subject to a shock wave from a clinical shock wave source. Advanced image processing was employed to extract the contour of the cell from the images. The evolution of the observed cell contour revealed a relatively small deformation during the compressional phase and a much larger deformation during the tensile phases of a shock wave. The experimental observations were captured by a numerical model which describes the volumetric cell response with a bilinear Equation of State and the deviatoric cell response with a viscoelastic framework. Experiments using human kidney cancer cells (CAKI-2) and noncancerous kidney cells (HRE and HK-2) were compared to the model in order to determine their mechanical properties. The differences between cancerous and noncancerous cells were exploited to demonstrate a design process by which shock waves may be able to improve the specificity on targeted cancer cells while having minimal effect on normal cells. The cell response to shock waves was studied in a more biophysically realistic environment to include influence of cell size, shape and orientation, and the presence of neighbouring cells. The most significant difference was predicted when cells were in a cluster in which case the presence of neighbouring cells resulted in a four-fold increase on the von Mises stress and the membrane strain. Finally the numerical model was extended to capture the effect of cell damage using one of two paradigms. In the first paradigm the model captured microdamage during one shock wave but then assumed that the cell recovered by the time the next shock wave arrived. The second model allowed microdamage to accumulate with increasing number of shock waves. These models may be able to explain the strong effect that shock wave loading rate has on tissue damage. In conclusion a validated numerical model has been developed which provides a mechanistic understanding of how cells respond to shock waves. The model has application in suggesting improved strategies for current uses of shock waves, e.g., lithotripsy, as well as opening up new indications such as cancer treatment.

First, we investigate the steady Euler flows through a general 3-D axially symmetric infinitely long nozzles without irrotationality. Global existence and uniqueness of subsonic solution are established, when the variation of Bernoulli's function in the upstream is sufficiently small and mass flux has an upper critical value. / Second, we concerns the following transonic shock phenomena in a class of de Laval nozzles with porous medium posed by Courant-Friedrichs: Given a appropriately large receiver pressure pr, if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed. The position and the strength of the shock front are automatically adjusted so that the end pressure at the exit becomes pr. We investigate this problem for the full Euler equations, the stability of the transonic shock is proved when the upstream supersonic flow is a small steady perturbation of the uniform supersonic flow and the corresponding pressure at the exit has a small perturbation. / Duan, Ben. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 125-137). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.