The class of hyperbolic conservation laws model the phenomena of non-linear wave propagation, including the presence and propagation of discontinuities and expansion waves. Such nonlinear systems can generate discontinuities in the so-lution even for smooth initial conditions. Presence of discontinuities results in break down of a solution in the classical sense and to show existence, weak for-mulation of a problem is required. Moreover, closed form solutions are di cult to obtain and in some cases such solutions are even unavailable. Thus, numerical algorithms play an important role in solving such systems. There are several dis-cretization techniques to solve hyperbolic systems numerically and Finite Volume Method (FVM) is one of such important frameworks. Numerical algorithms based on FVM are broadly classi ed into two categories, central discretization methods and upwind discretization methods. Various upwind and central discretization methods developed so far di er widely in terms of robustness, accuracy and ef-ciency and an ideal scheme with all these characteristics is yet to emerge. In this thesis, novel upwind and central schemes are formulated for various hyper-bolic systems, with the aim of maintaining right balance between accuracy and robustness. This thesis is divided into two parts. First part consists of the formulation of upwind methods to simulate genuine weakly hyperbolic (GWH) systems. Such systems do not possess full set of linearly independent (LI) eigenvectors and some of the examples include pressureless gas dynamics system, modi ed Burgers' sys-tem and further modi ed Burgers' system. The main challenge while formulating an upwind solver for GWH systems, using the concept of Flux Di erence Splitting (FDS), is to recover full set of LI eigenvectors, which is done through addition of generalized eigenvectors using the theory of Jordan Canonical Forms. Once the defective set of LI eigenvectors are completed, a novel (FDS-J) solver is for-mulated in such a manner that it is independent of generalized eigenvectors, as they are not unique. FDS-J solver is capable of capturing various shocks such as -shocks, 0-shocks and 00-shocks accurately. In this thesis, the FDS-J schemes are proposed for those GWH systems each of which have one particular repeated eigenvalue with arithmetic multiplicity (AM) greater than one. Moreover, each ux Jacobian matrix corresponding to such systems is similar to a unique Jordan matrix. After the successful treatment of genuine weakly hyperbolic systems, this strategy is further applied to those weakly hyperbolic subsystems which result on employ-ing various convection-pressure splittings to the Euler ux function. For example, Toro-Vazquez (TV) splitting and Zha-Bilgen (ZB) type splitting approaches to split the Euler ux function yield genuine weakly hyperbolic convective parts and strict hyperbolic pressure parts. Moreover, the ux Jacobian of each convective part is similar to a Jordan matrix with at least two lower order Jordan blocks. Based on the lines of FDS-J scheme, we develop two numerical schemes for Eu-ler equations using TV splitting and ZB type splitting. Both the new ZBS-FDS and TVS-FDS schemes are tested on various 1-D shock tube problems and out of two, contact capturing ZBS-FDS scheme is extended to 2-dimensional Euler system where it is tested successfully on various test cases including many shock instability problems. Second part of the thesis is associated with the development of simple, robust and accurate central solvers for systems of hyperbolic conservation laws. The idea of splitting schemes together with the notion of FDS is not easily extendable to systems such as shallow water equations. Thus, a novel central solver Convection Isolated Discontinuity Recognizing Algorithm (CIDRA) is formulated for shallow water equations. As the name suggests, the convective ux is isolated from the total ux in such a way that other ux, in present case other ux represents celerity part, must possess non-zero eigenvalue contribution. FVM framework is applied to each part separately and ux equivalence principle is used to x the coe cient of numerical di usion. CIDRA for SWE is computed on various 1-D and 2-D benchmark problems and extended to Euler systems e ortlessly. As a further improvement, a scalar di usion based algorithm CIDRA-1 is designed for v Euler systems. The scalar di usion coe cient depends on that particular part of the Rankine-Hugoniot (R-H) condition which involves total energy of the system as a direct contribution. This algorithm is applied to a variety of shock tube test cases including a class of low density ow problems and also to various 2-D test problems successfully. vi

L'étude de l'évolution de galaxies, et tout particulièrement du phénomène d'évaporation, a été pour la première fois menée à l'aide de modèles physiques, par Chandrasekhar notamment, dans les années 40. Depuis, de nouveaux modèles plus sophistiqués ont été introduits par les physiciens. Ces modèles d'évolution des galaxies sont des modèles cinétiques; bien connus et bien étudiés par les mathématiciens. Cependant, l'aspect évaporation (le fait que des étoiles sortent du système étudié) n'avait pas encore été étudié mathématiquement, à ma connaissance. La galaxie est vue comme un gaz constitué d'étoiles et le modèle consiste en une équation de Vlasov-Poisson, l'interaction étant la gravitation universelle, couplée avec au second membre un terme de collision de type Landau. On rajoute à ce modèle une condition d'évaporation qui consiste à dire que les étoiles dont l'énergie cinétique est suffisamment élevée pour quitter le système sont exclues. Ce modèle étant trop compliqué à étudier tel quel, je propose dans cette thèse plusieurs modèles simplifiés qui sont des premières étapes nécessaires à l'étude du modèle général et qui permettent de mieux comprendre les difficultés à surmonter. Dans une première partie, je m'intéresse au cas homogène en espace, pour lequel le terme de Vlasov-Poisson est remplacé par une simple dérivée en temps. Je fais une étude précise du cas à symétrie radiale en vitesse avec un potentiel Maxwellien, le terme de Landau étant alors remplacé par un terme de type Fokker-Planck, et je montre dans ce cas l'existence et l'unicité d'une solution régulière et l'existence d'un profil asymptotique des solutions. Dans le cas homogène général, je montre l'existence et l'unicité d'une solution régulière tout pendant que la masse ne s'est pas totalement évaporée. J'illustre ces résultats théoriques par des simulations numériques réalisés à l'aide de schéma numériques conservateurs. Dans une seconde partie, je m'intéresse au cas non homogène en espace en dérivant un modèle hydrodynamique pour un modèle de type Vlasov-BGK (plus simple que le modèle Vlasov-Poisson-Landau) avec évaporation. / The study of the evolution of the galaxies, and more specially of the evaporation phenomenon, was for the first time carried out, by Chandrasekhar in particular, in the 40s. Since then, more sophisticated models have been introduced by physicists. These models are kinetics models; well-known and well-studied by mathematicians. However, the evaporation (the fact that stars leave the galaxy) has never been studied before, to my knowledge. The galaxy is seen as a gaz of stars and the model is formed by a Vlasov-Poisson equation, with the gravitational interaction, coupled with Kernel of collision of Landau. A condition of evaporation is added to this model, saying the stars with a large enough kinetic energy are excluded. As this model is too complicated to be studied, I propose in this thesis several simpler models which constitute first steps toward the study of the general model and which inform us about the difficulties implied. In the first part, I am interested in the space-homogeneous model, for which the Vlasov-Poisson term is replaced by a simple time derivative. I make a precise study of the spherically symmetric case with a Maxwellian potential for which the the Landau term is replaced by a Fokker-Planck typed term, and I show the existence of a unique regular solution and the fact that this solution admits an asymptotical profile. In the general homogeneous case, I show the existence of a unique regular solution as long as the mass has not totally disappeared. Theses theoretical results are illustrated with numerical simulations obtained with conservative schemes. In the second part, I am interested in the inhomogeneous case and I derive an hydro-dynamical model for a Vlasov-BGK model (a simpler model than Vlasov-Poisson-Landau) with evaporation.

Tunable diode laser absorption spectroscopy using an external cavity diode laser operating in the infra-red has been developed to monitor CO2 in the freestream of the Longshot hypervelocity facility at the Von Karman Institute for Fluid Dynamics. The Longshot facility offers a unique European facility for ground testing and numerical validation applications, however, some of the traditional data rebuilding aspects are in question. A non-intrusive absorption<p>sensor could significantly aid in improving the knowledge of freestream static values thereby improving the models used in data rebuilding and numerical simulation. The design of such a sensor also expands the spectroscopic capabilities of the Von Karman Institute.<p><p>The absorption sensor is designed around the single P12 (00001)-(30013) rovibrational transition near 1.6µm (6218.09cm-1 specifically) which yields relatively weak direct absorption levels at about 3.5% per meter for typical Longshot freestream conditions. However, when handled carefully, adequate signal-to-noise can be acquired to exploit significant flow information. By being able to operate in this range, total sensor cost can be easily an a factor of two or more cheaper than sensors designed for the deeper infrared. All sensor elements were mounted to a compact portable optics bench utilizing single-mode optical fibers to allow for quick installation at different facilities by eliminating tedious optical realigning. Scans at 600Hz were performed over 20ms of the 40ms test time to extract core static temperature, pressure and velocity.<p><p>These results are compared with the current state of the Longshot data rebuild method. The non-uniform flow properties of the shear layer and test cabin rested gas accumulation was of an initial concern. The temperature and density gradients along with significant radial velocity components could result in DLAS temperature, pressure and velocity that are significantly different than that of the target freestream inviscid core values. Fortunately, with the proper selection of the P12 rotational number, this effect could be more or less ignored as the higher temperature and lower density gas of this region is relatively transparent.<p><p>Ultimately, acquired temperature and density were moderately accurate when compared to Longshot rebuilt results owing primarily to the baseline extraction which poses issues for such low absorption signals. However, the extracted velocity data are quite accurate. This is a definite puls for the sensor as the freestream enthalpy of cold hypersonic facilities is dictated primarily by the kinetic energy contribution. Being able to compare velocity gives insight to the level of vibration non-equilibrium in the flow. The velocity of the DLAS and the Longshot rebuild are quite close. This adds more weight to the argument that vibrational excitation is very low (if present at all) in the free stream and that the van de derWaals equation of state usage and constant specific heat assumption might be an adequate model for the data rebuild after all. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

A new discrete velocity scheme for solving the Boltzmann equation has been implemented for homogeneous relaxation and one-dimensional problems. Directly solving the Boltzmann equation is computationally expensive because in addition to working in physical space, the nonlinear collision integral must also be evaluated in a velocity space. To best solve the collision integral, collisions between each point in velocity space with all other points in velocity space must be considered, but this is very expensive. Motivated by the Direct Simulation Monte Carlo (DSMC) method, the computational costs in the present method are reduced by randomly sampling a set of collision partners for each point in velocity space. A collision partner selection algorithm was implemented to favor collision partners that contribute more to the collision integral. The new scheme has a built in flexibility, where the resolution in approximating the collision integral can be adjusted by changing how many collision partners are sampled. The computational cost associated with evaluation of the collision integral is compared to the corresponding statistical error. Having a fixed set of velocities can artificially limit the collision outcomes by restricting post collision velocities to those that satisfy the conservation equations and lie precisely on the grid. A new velocity interpolation algorithm enables us to map velocities that do not lie on the grid to nearby grid points while preserving mass, momentum, and energy. This allows for arbitrary post-collision velocities that lie between grid points or completely outside of the velocity space to be projected back onto the nearby grid points. The present scheme is applied to homogeneous relaxation of the non-equilibrium Bobylev Krook-Wu distribution, and the numerical results agree well with the analytic solution. After verifying the proposed method for spatially homogeneous relaxation problems, the scheme was then used to solve a 1D traveling shock. The jump conditions across the shock match the Rankine-Hugoniot jump conditions. The internal shock wave structure was then compared to DSMC solutions, and good agreement was found for Mach numbers ranging from 1.2 to 6. Since a coarse velocity discretization is required for efficient calculation, the effects of different velocity grid resolutions are examined. Although using a relatively coarse approximation for the collision integral is computationally efficient, statistical noise pollutes the solution. The effects of using coarse and fine approximations for the collision integral are examined and it is found that by coarsely evaluating the collision integral, the computational time can be reduced by nearly two orders of magnitude while retaining relatively smooth macroscopic properties. / text

Peat soils are known to be a significant source of atmospheric greenhouse gasses. However, the releases of methane and carbon dioxide gasses from peat soils are currently not well understood, particularly since the timing of the releases are poorly constrained. Furthermore, most research work performed on peatlands has been focused on temperate to sub-arctic peatlands, while recent works have suggested that gas production rates from low-latitude peat soils are higher than those from colder climates. The purpose of the work proposed here is to introduce an autonomous Ground Penetrating Radar (GPR) method for investigating the timing of gas releases from peat soils at the lab scale utilizing samples originating from Maine and the Florida Everglades, and at the field scale in a Maine peatland. Geophysical data are supported by direct gas flux measurements using the flux chamber method enhanced by timelapse photography, and terrestrial LiDAR (TLS) monitoring surface deformation. / by William J. Wright. / Thesis (M.S.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

Peat soils are known to be a significant emitter of atmospheric greenhouse gasses. However, the spatial and temporal variability in production and release of greenhouse gases (such as methane) in peat soils remains uncertain, particularly for low-latitude peatlands like the Florida Everglades, as the majority of studies on gas dynamics in peatlands focus on northern peatlands. The purpose of the work outlined here is focused on understanding the spatial and temporal variability in biogenic gas dynamics (i.e. production and release of methane and carbon dioxide) by implementing various experiments in the Florida Everglades at different scales of measurement, using noninvasive hydrogeophysical methods. Non-invasive methods include ground-penetrating radar (GPR), gas traps, time-lapse cameras, and hydrostatic pressure head measurements, that were constrained with direct measurements on soil cores like porosity, and gas composition using gas chromatography. By utilizing the measurements of in-situ gas volumes, we are able to estimate gas production using a mass balance approach, explore spatial and temporal variabilities of gas dynamics, and better constrain gas ebullition models. A better understanding of the spatial and temporal variability in gas production and release in peat soils from the Everglades has implications regarding the role of subtropical wetlands in the global carbon cycle, and can help providing better production and flux estimates to help global climate researchers improve their predictions and models for climate change. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Includes bibliographical references. / by Yoshiaki Kuwano. / M.S.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1981. / MICROFICHE COPY AVIALABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 118-119. / by Jane Ellen Martini. / M.S.

This thesis deals with the direct simulation Monte Carlo (DSMC) method of analysing gas flows. The DSMC method was initially proposed as a method for predicting rarefied flows where the Navier-Stokes equations are inaccurate. It has now been extended to near continuum flows. The method models gas flows using simulation molecules which represent a large number of real molecules in a probabilistic simulation to solve the Boltzmann equation. Molecules are moved through a simulation of physical space in a realistic manner that is directly coupled to physical time such that unsteady flow characteristics are modelled. Intermolecular collisions and moleculesurface collisions are calculated using probabilistic, phenomenological models. The fundamental assumption of the DSMC method is that the molecular movement and collision phases can be decoupled over time periods that are smaller than the mean collision time. Two obstacles to the wide spread use of the DSMC method as an engineering tool are in the areas of simulation configuration, which is the configuration of the simulation parameters to provide a valid solution, and the time required to obtain a solution. For complex problems, the simulation will need to be run multiple times, with the simulation configuration being modified between runs to provide an accurate solution for the previous run�s results, until the solution converges. This task is time consuming and requires the user to have a good understanding of the DSMC method. Furthermore, the computational resources required by a DSMC simulation increase rapidly as the simulation approaches the continuum regime. Similarly, the computational requirements of three-dimensional problems are generally two orders of magnitude more than two-dimensional problems. These large computational requirements significantly limit the range of problems that can be practically solved on an engineering workstation or desktop computer. The first major contribution of this thesis is in the development of a DSMC implementation that automatically adapts the simulation. Rather than modifying the simulation configuration between solution runs, this thesis presents the formulation of algorithms that allow the simulation configuration to be automatically adapted during a single run. These adaption algorithms adjust the three main parameters that effect the accuracy of a DSMC simulation, namely the solution grid, the time step and the simulation molecule number density. The second major contribution extends the parallelisation of the DSMC method. The implementation developed in this thesis combines the capability to use a cluster of computers to increase the maximum size of problem that can be solved while simultaneously allowing excess computational resources to decrease the total solution time. Results are presented to verify the accuracy of the underlying DSMC implementation, the utility of the solution adaption algorithms and the efficiency of the parallelisation implementation.

The macroscopic chemistry method for modelling non-equilibrium reacting gas flows with the direct simulation Monte Carlo (DSMC) method is developed and tested. In the macroscopic method, the calculation of chemical reactions is decoupled from the DSMC collision routine. The number of reaction events that must be performed in a cell is calculated with macroscopic rate expressions. These expressions use local macroscopic information such as kinetic temperatures and density. The macroscopic method is applied to a symmetrical diatomic gas. For each dissociation event, a single diatom is selected with a probability based on internal energy and is dissociated into two atoms. For each recombination event, two atoms are selected at random and replaced by a single diatom. To account for the dissociation energy, the thermal energies of all particles in the cell are adjusted. The macroscopic method differs from conventional collision-based DSMC chemistry procedures, where reactions are performed as an integral part of the collision routine. The most important advantage offered by the macroscopic method is that it can utilise reaction rates that are any function of the macroscopic flow conditions. It therefore allows DSMC chemistry calculations to be performed using rate expressions for which no conventional chemistry model may exist. Given the accuracy and flexibility of the macroscopic method, it has significant potential for modelling reacting non-equilibrium gas flows. The macroscopic method is tested by performing DSMC calculations and comparing the results to those obtained using conventional DSMC chemistry models and experimental data. The macroscopic method gives density profiles in good agreement with experimental data in the chemical relaxation region downstream of a strong shock. Within the shock where strongly non-equilibrium conditions prevail, the macroscopic method provides good agreement with a conventional chemistry model. For the flow over a blunt axisymmetric cylinder, which also exhibits strongly non-equilibrium conditions, the macroscopic method also gives reasonable agreement with conventional chemistry models. The ability of the macroscopic method to utilise any rate expression is demonstrated by using a two-temperature rate model that accounts for dissociation-vibration coupling effects that are important in non-equilibrium reacting flows. Relative to the case without dissociation-vibration coupling, the macroscopic method with the two-temperature model gives reduced dissociation rates in vibrationally cold flows, as expected. Also, for the blunt cylinder flow, the two-temperature model gives reduced surface heat fluxes, as expected. The macroscopic method is also tested with a number density dependent form of the equilibrium constant. For zero-dimensional chemical relaxation, the resulting relaxation histories are in good agreement with those provided by an exact Runge-Kutta solution of the relaxation behaviour. Reviews of basic DSMC procedures and conventional DSMC chemistry models are also given. A method for obtaining the variable hard sphere parameters for collisions between particles of different species is given. Borgnakke-Larsen schemes for modelling internal energy exchange are examined in detail. Both continuous rotational and quantised vibrational energy modes are considered. Detailed derivations of viscosity and collision rate expressions for the generalised hard sphere model of Hassan and Hash [Phys. Fluids 5, 738 (1993)] and the modified version of Macrossan and Lilley [J. Thermophys. Heat Transfer 17, 289 (2003)] are also given.