Aspects of Chiral Symmetry Breaking in Lattice QCD

Thesis (Ph.D.)--University of Washington, 2016-08

ICTM: an interval tessellation-based model for reliable topographic segmentation

This work introduces a tessellation-based model for the declivity analysis of geographic regions. The analysis of the relief declivity, which is embedded in the rules of the model, categorizes each tessellation cell, with respect to the whole considered region, according to the (positive, negative, null) sign of the declivity of the cell. Such information is represented in the states assumed by the cells of the model. The overall configuration of such cells allows the division of the region into subregions of cells belonging to a same category, that is, presenting the same declivity sign. In order to control the errors coming from the discretization of the region into tessellation cells, or resulting from numerical computations, interval techniques are used. The implementation of the model is naturally parallel since the analysis is performed on the basis of local rules. An immediate application is in geophysics, where an adequate subdivision of geographic areas into segments presenting similar topographic characteristics is often convenient.

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation

In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier-Stokes equations. For the discretization of the leading order terms, we propose employing the generalization of the symmetric version of the interior penalty method, originally developed for the numerical approximation of linear self-adjoint second-order elliptic partial differential equations. In order to solve the resulting system of nonlinear equations, we exploit a (damped) Newton-GMRES algorithm. Numerical experiments demonstrating the practical performance of the proposed discontinuous Galerkin method with higher-order polynomials are presented.

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation

In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier--Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I a posteriori bounds are derived for the estimation of the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated. This general approach leads to the design of economical finite element meshes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed approach will be presented.

Conversor de energia das ondas em energia elétrica com dispositivo de coluna de água oscilante: simulação numérica e estudo geométrico

Os oceanos representam um dos maiores recursos naturais, possuindo expressivo potencial energético, podendo suprir parte da demanda energética mundial. Nas últimas décadas, alguns dispositivos destinados à conversão da energia das ondas dos oceanos em energia elétrica têm sido estudados. No presente trabalho, o princípio de funcionamento do conversor do tipo Coluna de Água Oscilante, do inglês Oscillating Water Colum, (OWC) foi analisado numericamente. As ondas incidentes na câmara hidro-pneumática da OWC, causam um movimento alternado da coluna de água no interior da câmara, o qual produz um fluxo alternado de ar que passa pela chaminé. O ar passa e aciona uma turbina a qual transmite energia para um gerador elétrico. O objetivo do presente estudo foi investigar a influência de diferentes formas geométricas da câmara sobre o fluxo resultante de ar que passa pela turbina, que influencia no desempenho do dispositivo. Para isso, geometrias diferentes para o conversor foram analisadas empregando modelos computacionais 2D e 3D. Um modelo computacional desenvolvido nos softwares GAMBIT e FLUENT foi utilizado, em que o conversor OWC foi acoplado a um tanque de ondas. O método Volume of Fluid (VOF) e a teoria de 2ª ordem Stokes foram utilizados para gerar ondas regulares, permitindo uma interação mais realista entre o conversor, água, ar e OWC. O Método dos Volumes Finitos (MVF) foi utilizado para a discretização das equações governantes. Neste trabalho o Contructal Design (baseado na Teoria Constructal) foi aplicado pela primeira vez em estudos numéricos tridimensionais de OWC para fim de encontrar uma geometria que mais favorece o desempenho do dispositivo. A função objetivo foi a maximização da vazão mássica de ar que passa através da chaminé do dispositivo OWC, analisado através do método mínimos quadrados, do inglês Root Mean Square (RMS). Os resultados indicaram que a forma geométrica da câmara influencia na transformação da energia das ondas em energia elétrica. As geometrias das câmaras analisadas que apresentaram maior área da face de incidência das ondas (sendo altura constante), apresentaram também maior desempenho do conversor OWC. A melhor geometria, entre os casos desse estudo, ofereceu um ganho no desempenho do dispositivo em torno de 30% maior.

Beurteilung der geomechanischen Stabilität und Integrität von Endlagerbergwerken im Salzgebirge auf der Grundlage geologischer und ingenieurgeologischer Untersuchungen

Any safety assessment of a permanent repository for radioactive waste has to include an analysis of the geomechanical stability of the repository and integrity of the geological barrier. Such an analysis is based on geological and engineering geological studies of the site, on laboratory and in-situ experiments, and on numerical calculations. Central part of the safety analysis is the geomechanical modelling of the host rock. The model should simulate as closely as possible the conditions at the site and the behaviour of the rock (e.g., geology, repository geometry, initial rock stress, and constitutive models). On the basis of the geomechanical model numerical calculations are carried out using the finite-element method and an appropriate discretization of the repository and the host rock. The assessment of the repository stability and the barrier integrity is based on calculated stress and deformation and on the behaviour of the host rock measured and observed in situ. An example of the geomechanical analysis of the stability and integrity of the Bartensieben mine, a former salt mine, is presented. This mine is actually used as a repository for low level radioactive waste. The example includes all necessary steps of geological, engineering geological, and geotechnical investigations.

All-regime Lagrangian-Remap numerical schemes for the gas dynamics equations. Applications to the large friction and low Mach coefficients

In this talk, we propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations. By all regime, we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M, i.e. such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1. The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M. This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy. A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism. A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed. Then a simple and efficient semi implicit scheme is also proposed. The resulting scheme is stable under a CFL condition driven by the (slow) material waves and not by the (fast) acoustic waves and so verifies the all regime property. Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.

A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics

We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous P^3_{k}-P_{k-1} elements whereas the magnetic part of the equations is approximated by discontinuous P^3_{k}-P_{k+1} elements. We carry out a complete a-priori error analysis and prove that the energy norm error is convergent of order O(h^k) in the mesh size h. We also show that the method is able to correctly capture and resolve the strongest magnetic singularities in non-convex polyhedral domains. These results are verified in a series of numerical experiments.

An hr-adaptive discontinuous Galerkin method for advection-diffusion problems

We propose an adaptive mesh refinement strategy based on exploiting a combination of a pre-processing mesh re-distribution algorithm employing a harmonic mapping technique, and standard (isotropic) mesh subdivision for discontinuous Galerkin approximations of advection-diffusion problems. Numerical experiments indicate that the resulting adaptive strategy can efficiently reduce the computed discretization error by clustering the nodes in the computational mesh where the analytical solution undergoes rapid variation.

Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual (DWR) approach. Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator.

A class of domain decomposition preconditioners for hp-discontinuous Galerkin finite element methods

In this article we address the question of efficiently solving the algebraic linear system of equations arising from the discretization of a symmetric, elliptic boundary value problem using hp-version discontinuous Galerkin finite element methods. In particular, we introduce a class of domain decomposition preconditioners based on the Schwarz framework, and prove bounds on the condition number of the resulting iteration operators. Numerical results confirming the theoretical estimates are also presented.

High-order hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows

This article is concerned with the construction of general isotropic and anisotropic adaptive strategies, as well as hp-mesh refinement techniques, in combination with dual-weighted-residual a posteriori error indicators for the discontinuous Galerkin finite element discretization of compressible fluid flow problems.

Numerical enclosures of the optimal cost of the Kantorovitch’s mass transportation problem

International audience

Potencialidade do sensor Worldview II na detecção de hematita e goethita em solos tropicais

Dissertação (mestrado)—Universidade de Brasília, Instituto de Geociências, Programa de Pós-Graduação Stricto Sensu em Geociências Aplicadas, 2016.

Investigating the mesh dependency and upscaling of 3D grain-based models for the simulation of brittle fracture processes in low-porosity crystalline rock

The application of 3D grain-based modelling techniques is investigated in both small and large scale 3DEC models, in order to simulate brittle fracture processes in low-porosity crystalline rock. Mesh dependency in 3D grain-based models (GBMs) is examined through a number of cases to compare Voronoi and tetrahedral grain assemblages. Various methods are used in the generation of tessellations, each with a number of issues and advantages. A number of comparative UCS test simulations capture the distinct failure mechanisms, strength profiles, and progressive damage development using various Voronoi and tetrahedral GBMs. Relative calibration requirements are outlined to generate similar macro-strength and damage profiles for all the models. The results confirmed a number of inherent model behaviors that arise due to mesh dependency. In Voronoi models, inherent tensile failure mechanisms are produced by internal wedging and rotation of Voronoi grains. This results in a combined dependence on frictional and cohesive strength. In tetrahedral models, increased kinematic freedom of grains and an abundance of straight, connected failure pathways causes a preference for shear failure. This results in an inability to develop significant normal stresses causing cohesional strength dependence. In general, Voronoi models require high relative contact tensile strength values, with lower contact stiffness and contact cohesional strength compared to tetrahedral tessellations. Upscaling of 3D GBMs is investigated for both Voronoi and tetrahedral tessellations using a case study from the AECL’s Mine-by-Experiment at the Underground Research Laboratory. An upscaled tetrahedral model was able to reasonably simulate damage development in the roof forming a notch geometry by adjusting the cohesive strength. An upscaled Voronoi model underestimated the damage development in the roof and floor, and overestimated the damage in the side-walls. This was attributed to the discretization resolution limitations.