JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

An algorithm for the generation of non-uniform, locally-orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi/Delaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally-orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a-priori bounds on element size and shape. Grid-quality is further improved through the application of hill-climbing type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution type studies is discussed in detail.Comment: Final revisions, as per: Engwirda, D.: JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere, Geosci. Model Dev., 10, 2117-2140, https://doi.org/10.5194/gmd-10-2117-2017, 201

Three-Dimensional Network Model for Coupling~of~Fracture and Mass Transport in Quasi-Brittle Geomaterials

Dual three-dimensional networks of structural and transport elements were combined to model the effect of fracture on mass transport in quasi-brittle geomaterials. Element connectivity of the structural network, representing elasticity and fracture, was defined by the Delaunay tessellation of a random set of points. The connectivity of transport elements within the transport network was defined by the Voronoi tessellation of the same set of points. A new discretisation strategy for domain boundaries was developed to apply boundary conditions for the coupled analyses. The properties of transport elements were chosen to evolve with the crack opening values of neighbouring structural elements. Through benchmark comparisons involving non-stationary transport and fracture, the proposed dual network approach was shown to be objective with respect to element size and orientation

A Micromechanically-Informed Model of Thermal Spallation with Application to Propulsive Landing

During the propulsive landing of spacecraft, the retrorocket exhaust plume introduces the landing site surface to significant pressure and heating. Landing site materials include concrete on Earth and bedrock on other bodies, two highly brittle materials. During a landing event, defects and voids in the material grow due to thermal expansion and coalesce, causing the surface to disaggregate or spall. After a spall is freed from the surface, the material beneath it is exposed to the pressure and heat load until it spalls, continuing the cycle until engine shutdown. Spalls and debris entrained in the exhaust plume risk damaging the lander or nearby assets- a risk that increases for larger engines. The purpose of this work is to develop a micromechanically-informed model of thermal spallation to improve understanding of this process, in the context of propulsive landing. A preliminary simulation of landing site spallation, utilizing an empirical thermal spallation model, indicates that spallation may occur for human-scale Mars landers. This model, however, was developed for drilling through granite, which has a fundamentally different microstructure compared to typical landing sites, necessitating a more general approach. To that end, highly-detailed simulations of thermomechanical loading, applied to representative microstructures, inform a functional relationship between applied heat flux and spallation rate. These representative microstructures can be generated using an algorithm that has been validated for a wide variety of materials, including basalt from Gusev Crater, Mars.Ph.D

Aircraft Trajectory Planning Considering Ensemble Forecasting of Thunderstorms

Mención Internacional en el título de doctorConvective weather poses a major threat that compromises the safe operation of flights while inducing delay and cost. The aircraft trajectory planning problem under thunderstorm evolution is addressed in this thesis, proposing two novel heuristic approaches that incorporate uncertainties in the evolution of convective cells. In this context, two additional challenges are faced. On the one hand, studies have demonstrated that given the computational power available nowadays, the best way to characterize weather uncertainties is through ensemble forecasting products, hence compatibility with them is crucial. On the other hand, for the algorithms to be used during a flight, they must be fast and deliver results in a few seconds. As a first methodology, three variants of the Scenario-Based Rapidly-Exploring Random Trees (SB-RRTs) are proposed. Each of them builds a tree to explore the free airspace during an iterative and random process. The so-called SB-RRT, the SB-RRT∗ and the Informed SB-RRT∗ find point-to-point safe trajectories by meeting a user-defined safety threshold. Additionally, the last two techniques converge to solutions of minimum flight length. In a second instance, the Augmented Random Search (ARS) algorithm is used to sample trajectories from a directed graph and deform them iteratively in the search for an optimal path. The aim of such deformations is to adapt the initial graph to the unsafe set and its possible changes. In the end, the ARS determines the population of trajectories that, on average, minimizes a combination of flight time, time in storms, and fuel consumption Both methodologies are tested considering a dynamic model of an aircraft flying between two waypoints at a constant flight level. Test scenarios consist of realistic weather forecasts described by an ensemble of equiprobable members. Moreover, the influence of relevant parameters, such as the maximum number of iterations, safety margin (in SB-RRTs) or relative weights between objectives (in ARS) is analyzed. Since both algorithms and their convergence processes are random, sensitivity analyses are conducted to show that after enough iterations the results match. Finally, through parallelization on graphical processing units, the required computational times are reduced substantially to become compatible with near real-time operation. In either case, results show that the suggested approaches are able to avoid dangerous and uncertain stormy regions, minimize objectives such as time of flight, flown distance or fuel consumption and operate in less than 10 seconds.Los fenómenos convectivos representan una gran amenaza que compromete la seguridad de los vuelos, a la vez que incrementa los retrasos y costes. En esta tesis se aborda el problema de la planificación de vuelos bajo la influencia de tormentas, proponiendo dos nuevos métodos heurísticos que incorporan incertidumbre en la evolución de las células convectivas. En este contexto, se intentará dar respuesta a dos desafíos adicionales. Por un lado, hay estudios que demuestran que, con los recursos computacionales disponibles hoy en día, la mejor manera de caracterizar la incertidumbre meteorológica es mediante productos de tipo “ensemble”. Por tanto, la compatibilidad con ellos es crucial. Por otro lado, para poder emplear los algoritmos durante el vuelo, deben de ser rápidos y obtener resultados en pocos segundos. Como primera aproximación, se proponen tres variantes de los “Scenario-Based Rapidly-Exploring Random Trees” (SB-RRTs). Cada uno de ellos crea un árbol que explora el espacio seguro durante un proceso iterativo y aleatorio. Los denominados SB-RRT, SB-RRT∗ e Informed SB-RRT∗ calculan trayectorias entre dos puntos respetando un margen de seguridad impuesto por el usuario. Además, los dos últimos métodos convergen en soluciones de mínima distancia de vuelo. En segundo lugar, el algoritmo “Augmented Random Search” (ARS) se utiliza para muestrear trajectorias de un grafo dirigido y deformarlas iterativamente en busca del camino óptimo. El fin de tales deformaciones es adaptar el grafo inicial a las zonas peligrosas y a los cambios que puedan sufrir. Finalmente, el ARS calcula aquella población de trayectorias que, de media, minimiza una combinación del tiempo de vuelo, el tiempo en zonas tormentosas y el consumo de combustible. Ambas metodologías se testean considerando un modelo de avión volando punto a punto a altitud constante. Los casos de prueba se basan en datos meteorológicos realistas formados por un grupo de predicciones equiprobables. Además, se analiza la influencia de los parámetros más importantes como el máximo número de iteraciones, el margen de seguridad (en SB-RRTs) o los pesos relativos de cada objetivo (en ARS). Como ambos algoritmos y sus procesos de convergencia son aleatorios, se realizan análisis de sensibilidad para mostrar que, tras suficientes iteraciones, los resultados coinciden. Por último, mediante técnicas de paralelización en procesadores gráficos, se reducen enormemente los tiempos de cálculo, siendo compatibles con una operación en tiempo casi-real. En ambos casos los resultados muestran que los algoritmos son capaces de evitar zonas inciertas de tormenta, minimizar objetivos como el tiempo de vuelo, la distancia recorrida o el consumo de combustible, en menos de 10 segundos de ejecución.Programa de Doctorado en Ingeniería Aeroespacial por la Universidad Carlos III de MadridPresidente: Ernesto Staffetti Giammaria.- Secretario: Alfonso Valenzuela Romero.- Vocal: Valentin Polishchu

Particle hydrodynamics with tessellation techniques

Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems can be traced back to spurious surface effects across contact discontinuities, and to SPH's inherent prevention of mixing at the particle level. We here investigate a new fluid particle model where the density estimate is carried out with the help of an auxiliary mesh constructed as the Voronoi tessellation of the simulation particles instead of an adaptive smoothing kernel. This Voronoi-based approach improves the ability of the scheme to represent sharp contact discontinuities. We show that this eliminates spurious surface tension effects present in SPH and that play a role in suppressing certain fluid instabilities. We find that the new `Voronoi Particle Hydrodynamics' described here produces comparable results than SPH in shocks, and better ones in turbulent regimes of pure hydrodynamical simulations. We also discuss formulations of the artificial viscosity needed in this scheme and how judiciously chosen correction forces can be derived in order to maintain a high degree of particle order and hence a regular Voronoi mesh. This is especially helpful in simulating self-gravitating fluids with existing gravity solvers used for N-body simulations.Comment: 26 pages, 24 figures, currentversion is accepted by MNRA

Homogenization of the Linear and Non-linear Mechanical Behavior of Polycrystals

This work is dedicated to the numerically efficient simulation of the material response of polycrystalline aggregates. Therefore, crystal plasticity is combined with a new non-linear homogenization scheme, which is based on piecewise constant stress polarizations with respect to a homogeneous reference medium and corresponds to a generalization of the Hashin-Shtrikman scheme. This mean field approach accounts for the one- and two-point statistics of the microstructure

Homogenization of the Linear and Non-linear Mechanical Behavior of Polycrystals

This work is dedicated to the numerically efficient simulation of the material response of polycrystalline aggregates. Therefore, crystal plasticity is combined with a new non-linear homogenization scheme, which is based on piecewise constant stress polarizations with respect to a homogeneous reference medium and corresponds to a generalization of the Hashin-Shtrikman scheme. This mean field approach accounts for the one- and two-point statistics of the microstructure