NUMERICAL SIMULATION of CONVECTION-DIFFUSION PROBLEMS BY THE CONTROL-VOLUME-BASED FINITE-ELEMENT METHOD

This work presents a numerical study of the tri-dimensional convection-diffusion equation by the control-volume-based on finite-element method using quadratic hexahedral elements. Considering that the equation governing this problem in its main variable may represent several properties, including temperature, turbulent kinetic energy, viscous dissipation rate of the turbulent kinetic energy, specific dissipation rate of the turbulent kinetic energy, or even the concentration of a contaminant in a given medium, among others, the wide applicability of this problem is thus evidenced. Three cases of temperature distributions will be studied specifically in this work, in addition to one case of pollutant dispersion upon analysis of the concentration of a contaminant in a fixed flow point. Some comparisons will be carried out against works found in the open literature, while others will be done according to each phenomenon characteristics.

ITERATIVE NUMERICAL-SOLUTION OF SCATTERING PROBLEMS

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10(10) after some 8-10 iterations.

NUMERICAL AND ANALYTICAL VERIFICATION OF A MULTISCALE COMPUTATIONAL MODEL FOR IMPACT PROBLEMS IN HETEROGENEOUS VISCOELASTIC MATERIALS WITH EVOLVING DAMAGE

Composites are engineered materials that take advantage of the particular properties of each of its two or more constituents. They are designed to be stronger, lighter and to last longer which can lead to the creation of safer protection gear, more fuel efficient transportation methods and more affordable materials, among other examples. This thesis proposes a numerical and analytical verification of an in-house developed multiscale model for predicting the mechanical behavior of composite materials with various configurations subjected to impact loading. This verification is done by comparing the results obtained with analytical and numerical solutions with the results found when using the model. The model takes into account the heterogeneity of the materials that can only be noticed at smaller length scales, based on the fundamental structural properties of each of the composite’s constituents. This model can potentially reduce or eliminate the need of costly and time consuming experiments that are necessary for material characterization since it relies strictly upon the fundamental structural properties of each of the composite’s constituents. The results from simulations using the multiscale model were compared against results from direct simulations using over-killed meshes, which considered all heterogeneities explicitly in the global scale, indicating that the model is an accurate and fast tool to model composites under impact loads. Advisor: David H. Allen

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom-Pom model

This work presents numerical simulations of two fluid flow problems involving moving free surfaces: the impacting drop and fluid jet buckling. The viscoelastic model used in these simulations is the eXtended Pom-Pom (XPP) model. To validate the code, numerical predictions of the drop impact problem for Newtonian and Oldroyd-B fluids are presented and compared with other methods. In particular, a benchmark on numerical simulations for a XPP drop impacting on a rigid plate is performed for a wide range of the relevant parameters. Finally, to provide an additional application of free surface flows of XPP fluids, the viscous jet buckling problem is simulated and discussed. (C) 2011 Elsevier B.V. All rights reserved.

Fast and accurate numerical solutions in some problems of particle and radiation transport: synthetic acceleration for the method of short characteristics, Doppler-broadened scattering kernel, remote sensing of the cryosphere

The aim of this work is to present various aspects of numerical simulation of particle and radiation transport for industrial and environmental protection applications, to enable the analysis of complex physical processes in a fast, reliable, and efficient way. In the first part we deal with speed-up of numerical simulation of neutron transport for nuclear reactor core analysis. The convergence properties of the source iteration scheme of the Method of Characteristics applied to be heterogeneous structured geometries has been enhanced by means of Boundary Projection Acceleration, enabling the study of 2D and 3D geometries with transport theory without spatial homogenization. The computational performances have been verified with the C5G7 2D and 3D benchmarks, showing a sensible reduction of iterations and CPU time. The second part is devoted to the study of temperature-dependent elastic scattering of neutrons for heavy isotopes near to the thermal zone. A numerical computation of the Doppler convolution of the elastic scattering kernel based on the gas model is presented, for a general energy dependent cross section and scattering law in the center of mass system. The range of integration has been optimized employing a numerical cutoff, allowing a faster numerical evaluation of the convolution integral. Legendre moments of the transfer kernel are subsequently obtained by direct quadrature and a numerical analysis of the convergence is presented. In the third part we focus our attention to remote sensing applications of radiative transfer employed to investigate the Earth's cryosphere. The photon transport equation is applied to simulate reflectivity of glaciers varying the age of the layer of snow or ice, its thickness, the presence or not other underlying layers, the degree of dust included in the snow, creating a framework able to decipher spectral signals collected by orbiting detectors.

Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

The effect of boundary conditions in the numerical solution of 3-D thermoelastic problems

After the extensive research on the capabilities of the Boundary Integral Equation Method produced during the past years the versatility of its applications has been well founded. Maybe the years to come will see the in-depth analysis of several conflictive points, for example, adaptive integration, solution of the system of equations, etc. This line is clear in academic research. In this paper we comment on the incidence of the manner of imposing the boundary conditions in 3-D coupled problems. Here the effects are particularly magnified: in the first place by the simple model used (constant elements) and secondly by the process of solution, i.e. first a potential problem is solved and then the results are used as data for an elasticity problem. The errors add to both processes and small disturbances, unimportant in separated problems, can produce serious errors in the final results. The specific problem we have chosen is especially interesting. Although more general cases (i.e. transient)can be treated, here the domain integrals can be converted into boundary ones and the influence of the manner in which boundary conditions are applied will reflect the whole importance of the problem.

Problems for the numerical analysis of the future; [papers presented at the symposium on modern calculating machinery and numerical methods, held on July 29-31, 1948, at the University of California, Los Angeles]

Includes bibliographies.

The use of Illiac IV to solve numerical fluid dynamics problems : a status report /

Includes bibliographies (p. 50).

Numerical solution of flood prediction and river regulation problems; report.

Reports 2 and 3 by E. Isaacson, J. J. Stoker, and A. Troesch.

The approximate numerical solution of boundary value problems by relaxation methods,

"Contract N7 onr-358, T. O. I., NR-041-032."

Theoretical and numerical analysis of large-scale heat transfer problems with temperature-dependent pore-fluid densities

Purpose - In many scientific and engineering fields, large-scale heat transfer problems with temperature-dependent pore-fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large-scale heat transfer problems with temperature-dependent pore-fluid densities in the lithosphere and crust scales. Design/methodology/approach - The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts. Findings - From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive-and-advective lithosphere with variable pore-fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere. Originality/value - The present analytical solutions can be used to: validate numerical methods for solving large-scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large-scale heat transfer problems with temperature-dependent fluid densities.

Theory and application of inverse problems in groundwater: numerical, laboratory and field studies.

Aquifers are a vital water resource whose quality characteristics must be safeguarded or, if damaged, restored. The extent and complexity of aquifer contamination is related to characteristics of the porous medium, the influence of boundary conditions, and the biological, chemical and physical processes. After the nineties, the efforts of the scientists have been increased exponentially in order to find an efficient way for estimating the hydraulic parameters of the aquifers, and thus, recover the contaminant source position and its release history. To simplify and understand the influence of these various factors on aquifer phenomena, it is common for researchers to use numerical and controlled experiments. This work presents some of these methods, applying and comparing them on data collected during laboratory, field and numerical tests. The work is structured in four parts which present the results and the conclusions of the specific objectives.

Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.