Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics.

A novel time integration scheme is presented for the numerical solution of the dynamics of discrete systems consisting of point masses and thermo-visco-elastic springs. Even considering fully coupled constitutive laws for the elements, the obtained solutions strictly preserve the two laws of thermo dynamics and the symmetries of the continuum evolution equations. Moreover, the unconditional control over the energy and the entropy growth have the effect of stabilizing the numerical solution, allowing the use of larger time steps than those suitable for comparable implicit algorithms. Proofs for these claims are provided in the article as well as numerical examples that illustrate the performance of the method.

Accelerating CFD via local POD plus Galerkin projections

Se desarrollan varias técnicas basadas en descomposición ortogonal propia (DOP) local y proyección de tipo Galerkin para acelerar la integración numérica de problemas de evolución, de tipo parabólico, no lineales. Las ideas y métodos que se presentan conllevan un nuevo enfoque para la modelización de tipo DOP, que combina intervalos temporales cortos en que se usa un esquema numérico estándard con otros intervalos temporales en que se utilizan los sistemas de tipo Galerkin que resultan de proyectar las ecuaciones de evolución sobre la variedad lineal generada por los modos DOP, obtenidos a partir de instantáneas calculadas en los intervalos donde actúa el código numérico. La variedad DOP se construye completamente en el primer intervalo, pero solamente se actualiza en los demás intervalos según las dinámicas de la solución, aumentando de este modo la eficiencia del modelo de orden reducido resultante. Además, se aprovechan algunas propiedades asociadas a la dependencia débil de los modos DOP tanto en la variable temporal como en los posibles parámetros de que pueda depender el problema. De esta forma, se aumentan la flexibilidad y la eficiencia computacional del proceso. La aplicación de los métodos resultantes es muy prometedora, tanto en la simulación de transitorios en flujos laminares como en la construcción de diagramas de bifurcación en sistemas dependientes de parámetros. Las ideas y los algoritmos desarrollados en la tesis se ilustran en dos problemas test, la ecuación unidimensional compleja de Ginzburg-Landau y el problema bidimensional no estacionario de la cavidad. Abstract Various ideas and methods involving local proper orthogonal decomposition (POD) and Galerkin projection are presented aiming at accelerating the numerical integration of nonlinear time dependent parabolic problems. The proposed methods come from a new approach to the POD-based model reduction procedures, which combines short runs with a given numerical solver and a reduced order model constructed by expanding the solution of the problem into appropriate POD modes, which span a POD manifold, and Galerkin projecting some evolution equations onto that linear manifold. The POD manifold is completely constructed from the outset, but only updated as time proceeds according to the dynamics, which yields an adaptive and flexible procedure. In addition, some properties concerning the weak dependence of the POD modes on time and possible parameters in the problem are exploited in order to increase the flexibility and efficiency of the low dimensional model computation. Application of the developed techniques to the approximation of transients in laminar fluid flows and the simulation of attractors in bifurcation problems shows very promising results. The test problems considered to illustrate the various ideas and check the performance of the algorithms are the onedimensional complex Ginzburg-Landau equation and the two-dimensional unsteady liddriven cavity problem.

A characterization of conserved quantities in non-equilibrium thermodynamics

The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium thermodynamics formulated within the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) framework. The geometric meaning of symmetry is reviewed in this formal setting and then utilized to identify possible conserved quantities and the conditions that guarantee their strict conservation. Examples are provided that demonstrate the validity of the proposed definition in the context of finite and infinite dimensional thermoelastic problems.

Singularities in DROMO formulation. Analysis of deep flybys

The singularities in Dromo are characterized in this paper, both from an analytical and a numerical perspective. When the angular momentum vanishes, Dromo may encounter a singularity in the evolution equations. The cancellation of the angular momentum occurs in very speci?c situations and may be caused by the action of strong perturbations. The gravitational attraction of a perturbing planet may lead to rapid changes in the angular momentum of the particle. In practice, this situation may be encountered during deep planetocentric ?ybys. The performance of Dromo is evaluated in di?erent scenarios. First, Dromo is validated for integrating the orbit of Near Earth Asteroids. Resulting errors are of the order of the diameter of the asteroid. Second, a set of theoretical ?ybys are designed for analyzing the performance of the formulation in the vicinity of the singularity. New sets of Dromo variables are proposed in order to minimize the dependency of Dromo on the angular momentum. A slower time scale is introduced, leading to a more stable description of the ?yby phase. Improvements in the overall performance of the algorithm are observed when integrating orbits close to the singularity.

Energy-consistent time integration for nonlinear viscoelasticity

This work is concerned with the numerical solution of the evolution equations of thermomechanical systems, in such a way that the scheme itself satisfies the laws of thermodynamics. Within this framework, we present a novel integration scheme for the dynamics of viscoelastic continuum bodies in isothermal conditions. This method intrinsically satisfies the laws of thermodynamics arising from the continuum, as well as the possible additional symmetries. The resulting solutions are physically accurate since they preserve the fundamental physical properties of the model. Furthermore, the method gives an excellent performance with respect to robustness and stability. Proof for these claims as well as numerical examples that illustrate the performance of the novel scheme are provided

A temperature-based thermodynamically consistent integration scheme for discrete thermo-elastodynamics

The formulation of thermodynamically consistent (TC) time integration methods was introduced by a general procedure based on the GENERIC form of the evolution equations for thermo-mechanical problems. The use of the entropy was reported to be the best choice for the thermodynamical variable to easily provide TC integrators. Also the employment of the internal energy was proved to not involve excessive complications. However, attempts towards the use of the temperature in the design of GENERIC-based TC schemes have so far been unfruitful. This paper complements the said procedure to attain TC integrators by presenting a TC scheme based on the temperature as thermodynamical state variable. As a result, the problems which arise due to the use of the entropy are overcome, mainly the definition of boundary conditions. What is more, the newly proposed method exhibits the general enhanced numerical stability and robustness properties of the entropy formulation.

Decomposition driven interface evolution for layers of binary mixtures: I. Model dirivation and base states

A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surfacefilm of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological nonequilibrium thermodynamics for a general nonisothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analyzed.

Chaos in non lineal Alfven waves using the DNLS equations

The electro-dynamical tethers emit waves in structured denominated Alfven wings. The Derivative Nonlineal Schrödinger Equation (DNLS) possesses the capacity to describe the propagation of circularly polarized Alfven waves of finite amplitude in cold plasmas. The DNLS equation is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In this article is presented a theoretical and numerical analysis when the growth rate of the unstable wave is next to zero considering two damping models: Landau and resistive. The DNLS equation presents a chaotic dynamics when is consider only three wave truncation. The evolution to chaos possesses three routes: hard transition, period-doubling and intermittence of type I.

Building intuition of iron evolution during solar cell processing through analysis of different process models

An important aspect of Process Simulators for photovoltaics is prediction of defect evolution during device fabrication. Over the last twenty years, these tools have accelerated process optimization, and several Process Simulators for iron, a ubiquitous and deleterious impurity in silicon, have been developed. The diversity of these tools can make it difficult to build intuition about the physics governing iron behavior during processing. Thus, in one unified software environment and using self-consistent terminology, we combine and describe three of these Simulators. We vary structural defect distribution and iron precipitation equations to create eight distinct Models, which we then use to simulate different stages of processing. We find that the structural defect distribution influences the final interstitial iron concentration ([Fe-i]) more strongly than the iron precipitation equations. We identify two regimes of iron behavior: (1) diffusivity-limited, in which iron evolution is kinetically limited and bulk [Fe-i] predictions can vary by an order of magnitude or more, and (2) solubility-limited, in which iron evolution is near thermodynamic equilibrium and the Models yield similar results. This rigorous analysis provides new intuition that can inform Process Simulation, material, and process development, and it enables scientists and engineers to choose an appropriate level of Model complexity based on wafer type and quality, processing conditions, and available computation time.