Real gas flows in a duct

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This include flow in a duct of variable cross-section as well as flow with cylindrical or spherical symmetry, and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The scheme is applied with success to a problem involving the interaction of converging and diverging cylindrical shocks for four equations of state and to a problem involving the reflection of a converging shock.

Riemann solvers with primitive parameter vectors for two-dimensional compressible flows of a real gas

An analysis of averaging procedures is presented for an approximate Riemann solver for the equations governing the compressible flow of a real gas. This study extends earlier work for the Euler equations with ideal gases.

Free gravity waves and balanced dynamics

It is shown how a renormalization technique, which is a variant of classical Krylov–Bogolyubov–Mitropol’skii averaging, can be used to obtain slow evolution equations for the vortical and inertia–gravity wave components of the dynamics in a rotating flow. The evolution equations for each component are obtained to second order in the Rossby number, and the nature of the coupling between the two is analyzed carefully. It is also shown how classical balance models such as quasigeostrophic dynamics and its second-order extension appear naturally as a special case of this renormalized system, thereby providing a rigorous basis for the slaving approach where only the fast variables are expanded. It is well known that these balance models correspond to a hypothetical slow manifold of the parent system; the method herein allows the determination of the dynamics in the neighborhood of such solutions. As a concrete illustration, a simple weak-wave model is used, although the method readily applies to more complex rotating fluid models such as the shallow-water, Boussinesq, primitive, and 3D Euler equations.

Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.

Coupled Kelvin-wave and mirage-wave instabilities in semigeostrophic dynamics

A weak instability mode, associated with phase-locked counterpropagating coastal Kelvin waves in horizontal anticyclonic shear, is found in the semigeostrophic (SG) equations for stratified flow in a channel. This SG instability mode approximates a similar mode found in the Euler equations in the limit in which particle-trajectory slopes are much smaller than f/N, where f is the Coriolis frequency and N > f the buoyancy frequency. Though weak under normal parameter conditions, this instability mode is of theoretical interest because its existence accounts for the failure of an Arnol’d-type stability theorem for the SG equations. In the opposite limit, in which the particle motion is purely vertical, the Euler equations allow only buoyancy oscillations with no horizontal coupling. The SG equations, on the other hand, allow a physically spurious coastal “mirage wave,” so called because its velocity field vanishes despite a nonvanishing disturbance pressure field. Counterpropagating pairs of these waves can phase-lock to form a spurious “mirage-wave instability.” Closer examination shows that the mirage wave arises from failure of the SG approximations to be self-consistent for trajectory slopes f/N.

Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Application of a bounded upwinding scheme to complex fluid dynamics problems

This paper is concerned with an overview of upwinding schemes, and further nonlinear applications of a recently introduced high resolution upwind differencing scheme, namely the ADBQUICKEST [V.G. Ferreira, F.A. Kurokawa, R.A.B. Queiroz, M.K. Kaibara, C.M. Oishi, J.A.Cuminato, A.F. Castelo, M.F. Tomé, S. McKee, assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems, International Journal for Numerical Methods in Fluids 60 (2009) 1-26]. The ADBQUICKEST scheme is a new TVD version of the QUICKEST [B.P. Leonard, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Engineering 19 (1979) 59-98] for solving nonlinear balance laws. The scheme is based on the concept of NV and TVD formalisms and satisfies a convective boundedness criterion. The accuracy of the scheme is compared with other popularly used convective upwinding schemes (see, for example, Roe (1985) [19], Van Leer (1974) [18] and Arora & Roe (1997) [17]) for solving nonlinear conservation laws (for example, Buckley-Leverett, shallow water and Euler equations). The ADBQUICKEST scheme is then used to solve six types of fluid flow problems of increasing complexity: namely, 2D aerosol filtration by fibrous filters; axisymmetric flow in a tubular membrane; 2D two-phase flow in a fluidized bed; 2D compressible Orszag-Tang MHD vortex; axisymmetric jet onto a flat surface at low Reynolds number and full 3D incompressible flows involving moving free surfaces. The numerical simulations indicate that this convective upwinding scheme is a good generic alternative for solving complex fluid dynamics problems. © 2012.

The dynamics of a genetic algorithm for a simple learning problem

A formalism for describing the dynamics of Genetic Algorithms (GAs) using method s from statistical mechanics is applied to the problem of generalization in a perceptron with binary weights. The dynamics are solved for the case where a new batch of training patterns is presented to each population member each generation, which considerably simplifies the calculation. The theory is shown to agree closely to simulations of a real GA averaged over many runs, accurately predicting the mean best solution found. For weak selection and large problem size the difference equations describing the dynamics can be expressed analytically and we find that the effects of noise due to the finite size of each training batch can be removed by increasing the population size appropriately. If this population resizing is used, one can deduce the most computationally efficient size of training batch each generation. For independent patterns this choice also gives the minimum total number of training patterns used. Although using independent patterns is a very inefficient use of training patterns in general, this work may also prove useful for determining the optimum batch size in the case where patterns are recycled.

Analytic models of self-gravitating rotating gaseous tori with central black hole

In this thesis project, I present stationary models of rotating fluids with toroidal distributions that can be used to represent the active galactic nuclei (AGN) central obscurers, i.e. molecular tori (Combes et al., 2019), as well as geometrically thick accretion discs, like ADAF discs (Narayan and Yi, 1995) or Polish doughnuts (Abramowicz, 2005). In particular, I study stationary rotating systems with a more general baroclinic distribution (with a vertical gradient of the angular velocity), which are often more realistic and less studied, due to their complexity, than the barotropic ones (with cylindrical rotation), which are easier to construct. In the thesis, I compute analytically the main intrinsic and projected properties of the power-law tori based on the potential-density pairs of Ciotti and Bertin (2005). I study the density distribution and the resulting gravitational potential for different values of α, in the range 2 < α < 5. For the same models, I compute the surface density of the systems when seen face-on and edge-on. I then apply the stationary Euler equations to obtain rotational velocity and temperature distributions of the self-gravitating models in the absence of an external gravitational potential. In the thesis I also consider the power-law tori with the presence of a central black hole in addition to the gas self-gravity, and solving analytically the stationary Euler equations, I compute how the properties of the system are modified by the black hole and how they vary as a function of the black hole mass. Finally, applying the Solberg-Høiland criterion, I show that these baroclinic stationary models are linearly stable in the absence of the black hole. In the presence of the black hole I derive the analytical condition for stability, which depends on α and on the black hole mass. I also study the stability of the tori in the hypothesis that they are weakly magnetized, finding that they are always unstable to this instability.

Two-dimensional supersonic nonlinear Schrodinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schroumldinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ""ship-wave"" pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

Greenhouse gas emissions from alternative futures of deforestation and agricultural management in the southern Amazon

The Brazilian Amazon is one of the most rapidly developing agricultural areas in the world and represents a potentially large future source of greenhouse gases from land clearing and subsequent agricultural management. In an integrated approach, we estimate the greenhouse gas dynamics of natural ecosystems and agricultural ecosystems after clearing in the context of a future climate. We examine scenarios of deforestation and postclearing land use to estimate the future (2006-2050) impacts on carbon dioxide (CO(2)), methane (CH(4)), and nitrous oxide (N(2)O) emissions from the agricultural frontier state of Mato Grosso, using a process-based biogeochemistry model, the Terrestrial Ecosystems Model (TEM). We estimate a net emission of greenhouse gases from Mato Grosso, ranging from 2.8 to 15.9 Pg CO(2)-equivalents (CO(2)-e) from 2006 to 2050. Deforestation is the largest source of greenhouse gas emissions over this period, but land uses following clearing account for a substantial portion (24-49%) of the net greenhouse gas budget. Due to land-cover and land-use change, there is a small foregone carbon sequestration of 0.2-0.4 Pg CO(2)-e by natural forests and cerrado between 2006 and 2050. Both deforestation and future land-use management play important roles in the net greenhouse gas emissions of this frontier, suggesting that both should be considered in emissions policies. We find that avoided deforestation remains the best strategy for minimizing future greenhouse gas emissions from Mato Grosso.

The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

Lattice-gas model of orientable molecules: Application to liquid crystals

We have analyzed a two-dimensional lattice-gas model of cylindrical molecules which can exhibit four possible orientations. The Hamiltonian of the model contains positional and orientational energy interaction terms. The ground state of the model has been investigated on the basis of Karl¿s theorem. Monte Carlo simulation results have confirmed the predicted ground state. The model is able to reproduce, with appropriate values of the Hamiltonian parameters, both, a smectic-nematic-like transition and a nematic-isotropic-like transition. We have also analyzed the phase diagram of the system by mean-field techniques and Monte Carlo simulations. Mean-field calculations agree well qualitatively with Monte Carlo results but overestimate transition temperatures.

An algorithm for isentropic flow

An efficient algorithm is presented for the solution of the equations of isentropic gas dynamics with a general convex gas law. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only two function evaluations in each computational cell are required. The scheme is applied to a standard test problem in gas dynamics for a polytropic gas