Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 186-200). Also available in electronic version.

An attractive square-well is incorporated into the Enskog equation, in order to model the kinetic theory of a moderately dense gas with intermolecular potential. The existence of solutions to the Cauchy problem in <i>L</i>¹. global in time and for arbitrary initial data. is proved. A simple derivation of the square-well kinetic equation is given. Lewis's method is used~ which starts from the Liouville equation of statistical mechanics. Then various symmetries of the collisional integrals are established. An H-theorem for entropy, mass, and momentum conservation is obtained, as well as an energy estimate, and key gain-loss estimates. Approximate equations for the square-well kinetic equation are constructed that preserve symmetries of the collisional integral. Existence of nonnegative solutions of the approximate equations and weak compactness are obtained. The velocity averaging lemma of Golse is then a principal tool in demonstrating the convergence of the approximate solutions to a solution of the renormalized square well kinetic equation. The existence of weak solution of the initial value problem for the square well kinetic equation is thus proved. / Ph. D.

This thesis aimed at developing multi-scale models and computational methods for aerother-modynamics applications. The research on multi-scale models has focused on internal energy excitation and dissociation of molecular gases in atmospheric entry flows. The scope was two-fold: to gain insight into the dynamics of internal energy excitation and dissociation in the hydrodynamic regime and to develop reduced models for Computational Fluid Dynamics applications. The reduced models have been constructed by coarsening the resolution of a detailed rovibrational collisional model developed based on ab-initio data for the N2 (1Σ+g)-N (4Su) system provided by the Computational Quantum Chemistry Group at NASA Ames Research Center. Different mechanism reduction techniques have been proposed. Their appli-cation led to the formulation of conventional macroscopic multi-temperature models and vi-brational collisional models, and innovative energy bin models. The accuracy of the reduced models has been assessed by means of a systematic comparison with the predictions of the detailed rovibrational collisional model. Applications considered are inviscid flows behind normal shock waves, within converging-diverging nozzles and around axisymmetric bodies, and viscous flows along the stagnation-line of blunt bodies. The detailed rovibrational colli-sional model and the reduced models have been coupled to two flow solvers developed from scratch in FORTRAN 90 programming language (SHOCKING_F90 and SOLV-ER_FVMCC_F90). The results obtained have shown that the innovative energy bin models are able to reproduce the flow dynamics predicted by the detailed rovibrational collisional model with a noticeable benefit in terms of computing time. The energy bin models are also more accurate than the conventional multi-temperature and vibrational collisional models. The research on computational methods has focused on rarefied flows. The scope was to formu-late a deterministic numerical method for solving the Boltzmann equation in the case of multi-component gases with internal energy by accounting for both elastic and inelastic collisions. The numerical method, based on the weighted convolution structure of the Fourier trans-formed Boltzmann equation, is an extension of an existing spectral-Lagrangian method, valid for a mono-component gas without internal energy. During the development of the method, particular attention has been devoted to ensure the conservation of mass, momentum and en-ergy while evaluating the collision operators. Conservation is enforced through the solution of constrained optimization problems, formulated in a consistent manner with the collisional in-variants. The extended spectral-Lagrangian method has been implemented in a parallel com-putational tool (best; Boltzmann Equation Spectral Solver) written in C programming lan-guage. Applications considered are the time-evolution of an isochoric gaseous system initially set in a non-equilibrium state and the steady flow across a normal shock wave. The accuracy of the proposed numerical method has been assessed by comparing the moments extracted from the velocity distribution function with Direct Simulation Monte Carlo (DSMC) method predictions. In all the cases, an excellent agreement has been found. The computational results obtained for both space homogeneous and space inhomogeneous problems have also shown that the enforcement of conservation is mandatory for obtaining accurate numerical solutions.

It is well established that non-equilibrium flows cannot properly be described by traditional hydrodynamics, namely, the Navier-Stokes-Fourier (NSF) equations. Such flows occur, for example, in micro-electro-mechanical systems (MEMS), and ultra vacuum systems, where the dimensions of the devices are comparable to the mean free path of a gas molecule. Therefore, the study of non-equilibrium effects in gas flows is extremely important. The general interest of the present study is to explore boundary value problems for moderately rarefied gas flows, with an emphasis on numerical solutions of the regularized 13--moment equations (R13). Boundary conditions for the moment equations are derived based on either phenomenological principles or on microscopic gas-surface scattering models, e.g., Maxwell's accommodation model and the isotropic scattering model. Using asymptotic analysis, several non-linear terms in the R13 equations are transformed into algebraic terms. The reduced equations allow us to obtain numerical solutions for multidimensional boundary value problems, with the same set of boundary conditions for the linearized and fully non-linear equations. Some basic flow configurations are employed to investigate steady and unsteady rarefaction effects in rarefied gas flows, namely, planar and cylindrical Couette flow, stationary heat transfer between two plates, unsteady and oscillatory Couette flow. A comparison with the corresponding results obtained previously by the DSMC method is performed. The influence of rarefaction effects in the lid driven cavity problem is investigated. Solutions obtained from several macroscopic models, in particular the classical NSF equations with jump and slip boundary conditions, and the R13--moment equations are compared. The R13 results compare well with those obtained from more costly solvers for rarefied gas dynamics, such as the Direct Simulation Monte Carlo (DSMC) method. Flow and heat transfer in a bottom heated square cavity in a moderately rarefied gas are investigated using the R13 and NSF equations. The results obtained are compared with those from the DSMC method with emphasis on understanding thermal flow characteristics from the slip flow to the early transition regime. The R13 theory gives satisfying results including flow patterns in fair agreement with DSMC in the transition regime, which the conventional Navier-Stokes-Fourier equations are not able to capture. / Graduate / 0548 / anirudh@uvic.ca

Thesis (M. Sc.)--Carleton University, 2004. / Includes bibliographical references (p. 127-130). Also available in electronic format on the Internet.

学位授与大学：京都大学 ; 取得学位: 博士(工学) ; 学位授与年月日: 2007-09-25 ; 学位の種類: 新制・課程博士 ; 学位記番号: 工博第2860号 ; 請求記号: 新制/工/1420 ; 整理番号: 25545 / Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第13389号 / 工博第2860号 / 新制||工||1420(附属図書館) / 25545 / UT51-2007-Q790 / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 青木 一生, 教授 稲室 隆二, 教授 斧 髙一 / 学位規則第4条第1項該当

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第17512号 / 工博第3671号 / 新制||工||1558(附属図書館) / 30278 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 青木 一生, 教授 稲室 隆二, 教授 斧 髙一 / 学位規則第4条第1項該当

New upwind kinetic-difference schemes have been developed for flows with nonequilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Application of a directionally-split Courant-Isaacson-Rees (CIR) scheme at the Boltzmann level results in a flux-vector splitting scheme at the Euler level and is called Kinetic Flux-Vector Splitting (KFVS). Extension to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing non-equilibrium kinetic theory. Computational examples are presented comparing KFVS with the schemes of Van-Leer and Roe for quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, 'viscous flow over a cone at zero angle-of-attack, and shock-induced combustion/detonation in a premixed hydrogen-air mixture. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe. A new approach toward the development of a genuinely multi-dimensional Riemann solver is also presented. The scheme is based on the same kinetic theory considerations used in the development of the KF VS scheme. The work has been motivated by the recent progress on multi-dimensional upwind schemes by the groups at the University of Michigan and the Von Karman Institute. These researchers have developed effective upwind schemes for the multi-dimensional linear advection equation using a cell-vertex fluctuation-splitting approach on unstructured grids of triangles or tetrahedra. They have made preliminary applications to the Euler equations using several wave decomposition models of the flux derivative. The issue of the appropriate wave model does not appear to be adequately resolved. The approach taken in the present work is to apply these new multi-dimensional upwind schemes for the scalar advection equation at the Boltzmann level. The resulting Euler schemes are obtained as moments of the fluctuations in the Maxwellian distribution function. The development is significantly more complicated than standard (dimensionally-split) kinetic schemes in that the Boltzmann discretization depends upon the direction of the molecular velocities which must be accounted for in the limits of integration in velocity space. The theoretical issues have been solved through analytic quadrature and Euler schemes have been developed. For this formulation it was not necessary to prescribe any explicit wave decomposition model. Encouraging preliminary results have been obtained for perfect gases on uniform Cartesian meshes with first-order spatial accuracy. Results are presented for a 29° shock reflection, a 45° shear discontinuity, and Mach 3 flow over a step. Finally, methods for obtaining accurate gas-dynamic simulations in the continuum transition regime are considered. In particular, large departures from translational equilibrium are modeled using algorithms based on the Burnett equations instead of the Navier-Stokes equations. Here, the same continuum formulation of the governing equations is retained, but new constitutive relations based on higher-order Chapman-Enskog theory are introduced. Both a rotational relaxation model and a bulk-viscosity model have been considered for simulating rotational non-equilibrium. Results are presented for hypersonic normal shock calculations in argon and diatomic nitrogen and comparisons are made with Direct Simulation Monte Carlo (DSMC) results. The present work closely follows that of the group at Stanford, however, the use of upwind schemes and the bulk-viscosity model represent new contributions. / Ph. D.

A complete formulation of the recently developed. F_N method in kinetic theory is presented and the accuracy of this advanced semi-analytical-numerical technique is demonstrated by testing the method to several classical problems in rarefied gas dynamics. The method is based on the existing analysis for the vector transport equation arising from the decomposition of the linearized BGK equation. Using full-range orthogonality, a system of singular integral equations for the distribution functions at the boundaries is established. The unknown distribution functions are then approximated by a finite expansion in terms of a set of basis functions and the coefficients of the expansion are found by requiring the set of the reduced algebraic equations to be satisfied at certain collocation points. By studying the half-space heat transfer and weak evaporation problems and the problem of heat transfer between two parallel plates it is demonstrated that the F_N method is a viable solution technique yielding results of benchmark accuracy. Two different sets of basis functions are provided for half-space and finite media problems, respectively. In all cases, highly accurate numerical results are computed and compared to existing exact solutions. The obtained numerical results help in judging the accuracy to expect of the method and indicate that the F_N method may be applied with confidence to problems for which, more exact methods of analysis do not appear possible. Then, the cylindrical Poiseuille flow and thermal creep problems, which are not amenable to exact treatment, are solved. The F_N method is formulated and tested successfully for the first time in cylindrical geometry in kinetic theory. The complete solution of the two aforementioned problems is presented with the numerical results quoted as converged being of reference-quality good for benchmark accuracy. / Ph. D. / incomplete_metadata