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This dissertation discusses two aspects of computational fluid dynamics: high order spatial accuracy and convergence-rate acceleration through system preconditioning. Concerning high-order accuracy, the computational qualities of various spatial methods for the finite-volume solution of the Euler equations are presented. The two-dimensional essentially non-oscillatory (ENO), k-exact, and dimensionally split ENO reconstruction operators are discussed and compared in terms of reconstruction and solution accuracy and computational cost. Standard variable extrapolation methods are included for completeness. Inherent steady-state convergence difficulties are demonstrated for adaptive-stencil algorithms. Methods for reconstruction error analysis are presented and an exact solution to the heat equation is used as an example. Numerical experiments presented include the Ringleb flow for numerical accuracy and a shock-reflection problem. A vortex-shock interaction demonstrates the ability of the EN 0 scheme to excel in capturing unsteady high-frequency flow physics. Concerning convergence-rate acceleration, characteristic-wave preconditioning is extended to include generalized finite-rate chemistry with non-equilibrium thermodynamics Additionally, the proper preconditioning for the one-dimensional Navier-Stokes equations is presented. Eigenvalue stiffness is resolved and convergencerate acceleration is demonstrated over the entire Mach-number range from the incompressible to the hypersonic. Specific benefits are realized at low and transonic flow speeds. The extended preconditioning matrix accounts for thermal and chemical non-equilibrium and its implementation is explained for both explicit and implicit time marching. The effects of high-order spatial accuracy and various flux splittings are investigated. Numerical analysis reveals the possible theoretical improvements from using preconditioning at all Mach numbers. Numerical results confirm the expectations from the analysis. The preconditioning matrix is applied with dual time stepping to obtain arbitrarily high-order accurate temporal solutions within an implicit formulation. Representative test cases include flows with previously troublesome embedded high-condition-number regions. / Ph. D.

京都大学 / 新制・課程博士 / 博士(エネルギー科学) / 甲第25394号 / エネ博第473号 / 新制||エネ||88(附属図書館) / 京都大学大学院エネルギー科学研究科エネルギー基礎科学専攻 / (主査)教授 石澤 明宏, 教授 中村 祐司, 教授 稲垣 滋 / 学位規則第4条第1項該当 / Doctor of Energy Science / Kyoto University / DFAM

This thesis describes an experimental study on fluctuations of a Brownian particle immersed in a fluid, confined by optical tweezers and subject to two different kinds of non-equilibrium conditions. We aim to gain a rather general understanding of the relation between spontaneous fluctuations, linear response and total entropy production for processes away from thermal equilibrium. The first part addresses the motion of a colloidal particle driven into a periodic non-equilibrium steady state by a nonconservative force and its response to an external perturbation. The dynamics of the system is analyzed in the context of several generalized fluctuation-dissipation relations derived from different theoretical approaches. We show that, when taking into account the role of currents due to the broken detailed balance, the theoretical relations are verified by the experimental data. The second part deals with fluctuations and response of a Brownian particle in two different aging baths relaxing towards thermal equilibrium: a Laponite colloidal glass and an aqueous gelatin solution. The experimental results show that heat fluxes from the particle to the bath during the relaxation process play the same role of steady state currents as a non-equilibrium correction of the fluctuation-dissipation theorem. Then, the present thesis provides evidence that the total entropy production constitutes a unifying concept which links the statistical properties of fluctuations and the linear response function for non-equilibrium systems either in stationary or non stationary states.

In this thesis we show how reactive processes can be affected by the presence of different types of spatial constraints, so much so that their nonlinear dynamics can be qualitatively altered or that new and unexpected behaviors can be produced. To understand how this interplay can occur in general terms, we theoretically investigate four very different examples of this situation. <p><p>The first system we study is a reversible trimolecular chemical reaction which is taking place in closed one-dimensional lattices. We show that the low dimensionality may or may not prevent the reaction from reaching its equilibrium state, depending on the microscopic properties of the molecular reactive mechanism. <p><p>The second reactive process we consider is a network of biological interactions between pigment cells on the skin of zebrafish. We show that the combination of short-range and long-range contact-mediated feedbacks can promote a Turing instability which gives rise to stationary patterns in space with intrinsic wavelength, without the need of any kind of motion.<p><p>Then we investigate the behavior of a typical chemical oscillator (the Brusselator) when it is constrained in a finite space. We show that molecular crowding can in such cases promote new nonlinear dynamical behaviors, affect the usual ones or even destroy them. <p><p>Finally we look at the situation where the constraint is given by the presence of a solid porous matrix that can react with a perfect gas in an exothermic way. We show on one hand that the interplay between reaction, heat flux and mass transport can give rise to the propagation of adsorption waves, and on the other hand that the coupling between the chemical reaction and the changes in the structural properties of the matrix can produce sustained chemomechanical oscillations. <p><p>These results show that spatial constraints can affect the kinetics of reactions, and are able to produce otherwise absent nonlinear dynamical behaviors. As a consequence of this, the usual understanding of the nonlinear dynamics of reactive systems can be put into question or even disproved. In order to have a better understanding of these systems we must acknowledge that mechanical and structural feedbacks can be important components of many reactive systems, and that they can be the very source of complex and fascinating phenomena.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished