High performance of the generalized finite difference method and applications

[ES] En esta tesis se aborda la resolución de ecuaciones en derivadas parciales de segundo orden en 2D y 3D por el Método de las Diferencias Finitas Generalizadas (MDFG) utilizando aproximaciones de tercer y cuarto orden. En primer lugar, se analiza la influencia del número de puntos por estrella y se establecen algunos valores a modo de referencia. En segundo lugar, se ha desarrollado una nueva estrategia para detectar y tratar estrellas mal condicionadas, las cuales pueden aparecer con frecuencia cuando se utilizan aproximaciones de orden superior. Esta estrategia utiliza una cantidad de puntos por estrella menor que los establecidos como referencia y presenta excelentes resultados detectando estrellas mal condicionadas, aumentando la precisión de la aproximación numérica y reduciendo el coste computacional. Para implementar el algoritmo, se han utilizado buenas prácticas de programación junto con las aproximaciones de orden superior en el MDFG para reducir el coste computacional en diferentes etapas del cálculo. Por otro lado, se ha desarrollado una estrategia para obtener discretizaciones adaptadas al problema concreto que se desea resolver. Esta estrategia distribuye los puntos en el dominio conforme a los valores del gradiente, lo que permite usar una discretización con un menor número de puntos, reduciendo así el coste computacional y manteniendo la precisión que se alcanzaría con discretizaciones más finas donde los puntos se distribuyen más homogéneamente. Además, se ha desarrollado un algoritmo adaptativo para problemas en 3D con aproximaciones de cuarto orden a partir de discretizaciones iniciales irregulares. Se han comparado los resultados del algoritmo propuesto con los del algoritmo de puntos añadidos a media distancia. En todas las aplicaciones, se ha conseguido una mayor precisión junto con una disminución del número final de puntos y del tiempo computacional. Finalmente, para probar el desempeño del algoritmo en un problema real se ha evaluado la respuesta sísmica en aerogeneradores terrestres empleando el MDFG acoplado con el método de Newmark. Se han comparado los datos del desplazamiento transversal con un modelo basado en el método de los elementos finitos utilizando el programa ABAQUS. Los resultados son esencialmente idénticos y muestran la validez del modelo propuesto en el MDFG

A Novel Meshless Method Based on the Virtual Construction of Node Control Domains for Porous Flow Problems

In this paper, a novel meshless method that can handle porous flow problems with singular source terms is developed by virtually constructing the node control domains. By defining the connectable node cloud, this novel meshless method uses the integral of the diffusion term and generalized difference operators to derive overdetermined equations of the node control volumes. An empirical method of calculating reliable node control volumes and a triangulation-based method to determine the connectable point cloud are developed. NCDMM only focuses on the volume of the node control domain rather than the specific shape, so the construction of node control domains is called virtual, which will not increase the computational cost. To our knowledge, this is the first time to construct node control volumes in the meshless framework, so this novel method is named a node control domains-based meshless method, abbreviated as NCDMM, which can also be regarded as an extended finite volume method (EFVM). Taking two-phase porous flow problems as an example, the NCDMM discrete schemes meeting local mass conservation are derived by integrating the generalized finite difference schemes of governing equations on each node control domain. Finally, existing commonly used low-order finite volume method (FVM) based nonlinear solvers for various porous flow models can be directly employed in the proposed NCDMM, significantly facilitating the general-purpose applications of the NCDMM. Four numerical cases are implemented to test the computational accuracy, efficiency, convergence, and good adaptability to the calculation domain with complex geometry and various boundary conditions

A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs

We introduce a meshless method derived by considering the time variable as a spatial variable without the need to extend further conditions to the solution of linear and non-linear parabolic PDEs. The method is based on a moving least squares method, more precisely, the generalized finite difference method (GFDM), which allows us to select well-conditioned stars. Several 2D and 3D examples, including the time variable, are shown for both regular and irregular node distributions. The results are compared with explicit GFDM both in terms of errors and execution time

5 G Systems

Communication is an interactive dynamic, information that is continually at change. Especially in the eld of telecommunications, as time passed and with the appearance of First Generation, that allowed us to give mobility to Analog Communication...La comunicación es una dinámica interactiva debido a la constante evolución de la información. Especialmente en el campo de las telecomunicaciones, con el paso del tiempo y con la aparición de la Primera Generación y que nos permitió dar movilidad a la Comunicación Analógica..

Direct solution of Navier-Stokes equations by using an upwind local RBF-DQ method

The differential quadrature (DQ) method is able to obtain quite accurate numerical solutions of differential equations with few grid points and less computational effort. However, the traditional DQ method is convenient only for regular regions and lacks upwind mechanism to characterize the convection of the fluid flow. In this paper, an upwind local radial basis function-based DQ (RBF-DQ) method is applied to solve the Navier-Stokes equations, instead of using an iterative algorithm for the primitive variables. The non-linear collocated equations are solved using the Levenberg-Marquardt method. The irregular regions of 2D channel flow with different obstructions situations are considered. Finally, the approach is validated by comparing the results with those obtained using the well-validated Fluent commercial package

6G Wireless Systems: Vision, Requirements, Challenges, Insights, and Opportunities

Mobile communications have been undergoing a generational change every ten years or so. However, the time difference between the so-called "G's" is also decreasing. While fifth-generation (5G) systems are becoming a commercial reality, there is already significant interest in systems beyond 5G, which we refer to as the sixth-generation (6G) of wireless systems. In contrast to the already published papers on the topic, we take a top-down approach to 6G. We present a holistic discussion of 6G systems beginning with lifestyle and societal changes driving the need for next generation networks. This is followed by a discussion into the technical requirements needed to enable 6G applications, based on which we dissect key challenges, as well as possibilities for practically realizable system solutions across all layers of the Open Systems Interconnection stack. Since many of the 6G applications will need access to an order-of-magnitude more spectrum, utilization of frequencies between 100 GHz and 1 THz becomes of paramount importance. As such, the 6G eco-system will feature a diverse range of frequency bands, ranging from below 6 GHz up to 1 THz. We comprehensively characterize the limitations that must be overcome to realize working systems in these bands; and provide a unique perspective on the physical, as well as higher layer challenges relating to the design of next generation core networks, new modulation and coding methods, novel multiple access techniques, antenna arrays, wave propagation, radio-frequency transceiver design, as well as real-time signal processing. We rigorously discuss the fundamental changes required in the core networks of the future that serves as a major source of latency for time-sensitive applications. While evaluating the strengths and weaknesses of key 6G technologies, we differentiate what may be achievable over the next decade, relative to what is possible.Comment: Accepted for Publication into the Proceedings of the IEEE; 32 pages, 10 figures, 5 table

Nicht-oszillierende Verfahren höherer Ordnung unter Verwendung von Interpolating Moving Least Squares Rekonstruktion für hyperbolische Erhaltungssätze

Meshfree methods have attracted much attention for the development and their applications in the recent years. The methods are commonly formulated using the Moving Least Squares (MLS) methods. The interpolation version of the methods is determined by introducing the singular weight functions for constructing the shape functions and called as Interpolating Moving Least Squares (IMLS) methods. Since the shape functions of the IMLS interpolants satisfy the Kronecker delta, the IMLS methods have the property of nodal interpolation. For more information of the IMLS method the explicit formulae of the derivatives of the IMLS interpolants are derived. The methods are applied to a linear scalar conservation law with the Euler and Lax-Wendroff time discretizations. The higher order schemes are presented employing a Taylor series expansion. The field variables and their successive derivatives are reconstructed using the IMLS methods. An analysis of the L_2-norm of this method is given. The Weighted Essentially Non-Oscillatory (WENO) schemes are adopted in the new schemes to prevent spurious oscillation. Our new methods based on staggered grids are discretized on space and the central Runge-Kutta schemes are used for time integration. Numerical results show that our new methods achieve the expected accuracy from an analysis of L_2-norm. Representative simulations show that the proposed methods are applicable to hyperbolic conservation laws.In den letzten Jahren stieg das Interesse für die Entwicklung und Anwendung der netzfreien Verfahren an. Diese Verfahren basieren im Allgemeinen auf der Moving Least Square (MLS) Methode. Die interpolierende Form wird durch die Einführung einer singulären gewichteten Funktion bestimmt, um eine Kernfunktion, die so genannte IMLS Methode, aufzubauen. Die IMLS Methode mit ihrer Kernfunktion erfüllt die Kronecker Delta Eigenschaft und besitzt zugleich die Merkmale der Knoten-Interpolation. Um die IMLS Methode genauer zu untersuchen, wird die explizite Formel der IMLS Ableitung hergeleitet. Diese Verfahren finden in den linearen skalaren Erhaltungssätzen mit Euler- und Lax-Wendroff- Zeitintegration Anwendung. Ein Verfahren höherer Ordnung wird über der Taylor Entwicklung vorgestellt. Dabei werden die Variablen und die aufeinander folgenden Ableitungen anhand der IMLS Methode rekonstruiert. Eine Analyse der L2-Norm der Methode wird dargestellt. Die gewichteten wesentlich nichtoszillierenden Verfahren werden an die neue Methode angepasst um Oszillationen zu vermeiden. Das neue Verfahren, das auf versetzten Gittern basiert, wird für die Raum-Diskretisierung, und die zentrale Runge-Kutta Verfahren für die Zeit-Integration benutzt. Die numerischen Ergebnisse dieser Methode zeigen eine der L2-Norm-Analyse entsprechende Genauigkeit. Repräsentative Simulationen zeigen, dass die vorgeschlagene Methode auf hyperbolische Erhaltungsgleichungen angewendet werden kann

Discontinuous mechanical problems studied with a Peridynamics-based approach

The classical theory of solid mechanics is rooted in the assumption of a continuous distribution of mass within a body. It employs partial differential equations (PDEs) with significant smoothness to obtain displacements and internal forces of the body. Although classical theory has been applied to wide range of engineering problems, PDEs of the classical theory cannot be applied directly on a discontinuity such as cracks. Peridynamics is considered to be an alternative and promising nonlocal theory of solid mechanics that, by replacing PDEs of classical theory with integral or integro-differential equations, attempts to unite the mathematical modelling of continuous media, cracks and particles within a single framework. Indeed, the equations of peridynamic are based on the direct interaction of material points over finite distances. Another concept, derived from the peridynamic approach to cope with engineering problems with discontinuities, is that of the peridynamic differential operator (PDDO). The PDDO uses the non-local interaction of the material points in a way similar to that of peridynamics. PDDO is capable to recast partial derivatives of a function through a nonlocal integral operator whose kernel is free of using any correction function. In this dissertation, application of peridaynamics and PDDO, to three different important engineering problems including fatigue fracture, thermo-mechanics and sloshing phenomena, is examined comprehensively. To cope with fatigue fracture problems, an algorithm has been developed in such a way that the increment of damage due to fatigue is added to that due to the static increment of the opening displacement. A one degree of freedom cylinder model has been used to carry out an efficient comparison of the computational performance of three fatigue degradation strategies. The three laws have been implemented in a code using bond based peridynamics (BBPD) to simulate fatigue crack propagation. Both the cylinder model and the bond base peridynamics code provide the same assessment of the three fatigue degradation strategies. To deal with thermo-mechanical problems, an effective way is proposed to use a variable grid size in a weakly coupled thermal shock peridynamic model. The proposed numerical method is equipped with stretch control criterion to transform the grid discretization adaptively in time. Hence, finer grid spacing is only applied in limited zones where it is required. This method is capable of predicting complex crack patterns in the model. By introducing fine grid discretization over the boundaries of the model the surface (softening) effect can be reduced. The accuracy and performance of the model are examined through problems such as thermo-elastic and thermal-shock induced fracture in ceramics. Finally to investigate sloshing phenomena, the PDDO has been applied to the solution of problems of liquid sloshing in 2D and 3D tanks with potential flow theory and Lagrangian description. Moreover, liquid sloshing in rectangular tanks containing horizontal and vertical baffles are investigated to examine the robustness and accuracy of PDDO. With respect to other approaches such as meshless local Petrov-Galerkin (MLPG), volume of fluid (VOF) and and local polynomial collocation methods the examples are solved with a coarser grid of nodes. Using this new approach, one is able to obtain results with a high accuracy and low computational cost

Design, Simulation, Manufacturing: The Innovation Exchange

This book reports on topics at the interface between manufacturing, mechanical and chemical engineering. It gives a special emphasis to CAD/CAE systems, information management systems, advanced numerical simulation methods and computational modeling techniques, and their use in product design, industrial process optimization and in the study of the properties of solids, structures and fluids. Control theory, ICT for engineering education as well as ecological design and food technologies are also among the topics discussed in the book. Based on the International Conference on Design, Simulation, Manufacturing: The Innovation Exchange (DSMIE-2018), held on June 12-15, 2018, in Sumy, Ukraine, the book provides academics and professionals with a timely overview and extensive information on trends and technologies behind current and future developments of Industry 4.0, innovative design and renewable energy generation

From Mesh to Meshless : a Generalized Meshless Formulation Based on Riemann Solvers for Computational Fluid Dynamics

Programa Oficial de Doutoramento en Enxeñaría Civil . 5011V01[Abstract] From mesh to meshless: A generalized meshless formulation based on Riemann solvers for Computational Fluid Dynamics This thesis deals with the development of high accuracy meshless methods for the simulation of compressible and incompressible flows. Meshless methods were conceived to overcome the constraints that mesh topology impose on traditional mesh-based numerical methods. Despite the fact that meshless methods have achieved a relative success in some particular applications, the truth is that mesh-based methods are still the preferred choice to compute flows that demand high-accuracy. Instead of assuming that meshless and mesh-based methods are groups of methods that follow independent development paths, in this thesis it is proposed to increase the accuracy of meshless methods by taking guidance of some successful techniques adopted in the mesh-based community. The starting point for the development is inspired by the SPH-ALE scheme proposed by Vila. Especially, the flexibility of the ALE framework and the introduction of Riemann solvers are essential elements adopted. High accuracy is obtained by using the Moving Least Squares (MLS) technique. MLS serves multiple tasks in the implemented scheme: high order reconstruction of Riemann states, more accurate viscous flux evaluation and the replacement of the limited kernel approximation by MLS approximation with polynomial degree consistency by design. The stabilization of the scheme for compressible flows with discontinuities is based on a posteriori stabilization technique (MOOD) that introduces a great improvement compared with the traditional a priori flux limiters. The MLSPH-ALE scheme is the first proposed meshless formulation that uses high order consistent MLS approximation in a versatile ALE framework. In addition, the procedure to obtain the semi-discrete formulation keeps track of a boundary term, which eases the implementation of the boundary conditions. Another important contribution is related with the general concept of the MLSPHALE formulation. The MLSPH-ALE scheme is proved to be a global meshless formulation that under some particular settings provides the same semi-discrete equations that other meshless formulations published. The MLSPH-ALE scheme has been tested for the computation of turbulent flows. The low dissipation inherent to the Riemann solver is compatible with the implicit LES turbulent model. The proposed formulation is able to capture the energy cascade in the subsonic regime where traditional SPH formulations are reported to fail.[Resumen] Desde métodos con malla a métodos sin malla: Una formulación sin malla generalizada basada en solvers de Riemann para Dinámica de Fluidos Computacional Esta tesis aborda el desarrollo de métodos sin malla de alta precisión para la simulación de flujos compresibles e incompresibles. Los métodos sin malla fueron creados para superar las restricciones que la conectividad de la malla impone a los métodos tradicionales. A pesar de haber alcanzado un ´éxito relativo en algunas aplicaciones, la realidad es que los métodos con malla siguen siendo la opción preferida para el cálculo de flujos que demandan alta precisión. En vez de asumir que métodos sin malla y con malla son grupos de métodos que siguen caminos de desarrollo independientes, en esta tesis se propone incrementar la precisión de los métodos sin malla tomando como guía algunas de las técnicas más exitosas empleadas en la comunidad de los métodos con malla. El punto de partida para el desarrollo se inspira en el esquema SPH-ALE propuesto por Vila. De manera especial, la flexibilidad del marco de referencia ALE y la introducción de los solvers de Riemann son elementos esenciales adoptados. La alta precisión se obtiene con la técnica de Mínimos Cuadrados Móviles (MLS). MLS sirve múltiples funciones en la implementación del esquema: alto orden de reconstrucción de los estados de Riemann, evaluaciones más precisas de los flujos viscosos y reemplazo de la aproximación limitada tipo kernel por una aproximación MLS con un grado de consistencia polinómica arbitraria. La estabilización del esquema para flujos compresibles con discontinuidades se basa en una técnica de estabilización a posteriori (MOOD) que introduce una importante mejora con respecto a los tradicionales limitadores de flujo a priori. El esquema MLSPH-ALE es la primera formulación sin malla propuesta que utiliza la aproximación MLS de alto orden en un marco de referencia ALE. Además, el procedimiento dado para obtener la forma semi-discreta realiza el seguimiento de un término en la frontera del dominio que facilita la implementación discreta de las condiciones de contorno. Otra importante contribución está relacionada con el concepto general de la formulación MLSPH-ALE. Se ha demostrado que el esquema MLSPH-ALE es una formulación sin malla global que con ciertas configuraciones particulares es capaz de proporcionar las mismas formas semi-discretas que otras formulaciones publicadas. El método MLSPH-ALE ha sido puesto a prueba frente al cálculo de flujos turbulentos. La baja disipación inherente a los solver de Riemann hace que el esquema sea apto para modelar la turbulencia en un contexto de modelos implícitos LES. La formulación propuesta es capaz de capturar la cascada de energía en el rango de régimen subsónico donde los métodos tradicionales presentan fallos.[Resumo] Desde métodos con malla a métodos sen malla: Unha formulación sen malla xeneralizada baseada en solvers de Riemann para Dinámica de Fluidos Computacional. Esta tese trata sobre o desenvolvemento de métodos sen malla de alta precisión para a simulación de fluxos compresibles e incompresibles. Os métodos sen malla foron creados para superar as restricións que a conectividade da malla impón sobre os métodos tradicionais. A pesar de ter acadado un éxito relativo nalgunhas aplicacións, a realidade é que os métodos con malla seguen sendo a opción preferente para o cálculo de fluxos que demandan alta precisión. No canto de asumir que os métodos sen malla e con malla son grupos que seguen camiños de desenvolvemento independentes, nesta tese proponse incrementar a precisión dos métodos sen malla tomando como guía algunha das técnicas de máis éxito empregadas na comunidade dos métodos con malla. O punto de partida para o desenvolvemento inspírase no esquema SPH-ALE proposto por Vila. A flexibilidade do marco de referencia ALE e a introducción dos solvers de Riemann son os elementos esenciais utilizados nesta tese. A alta precisión acádase coa técnica de Mínimos Cadrados Móbiles (MLS). MLS serve para múltiples tarefas na implementación do esquema: acadar alto orde de reconstrución nos estados de Riemann, avaliacións máis precisas dos fluxos viscosos e troco da aproximación limitada tipo kernel por unha aproximación MLS con grado de consistencia polinómica arbitraria. A estabilización do esquema para fluxos compresibles con descontinuidades baséase nunha técnica de estabilización a posteriori (MOOD) que introduce unha importante mellora con respecto a os tradicionais limitadores de fluxo a priori. O esquema MLSPH-ALE ´e a primeira formulación sen malla proposta que emprega a técnica de aproximación MLS con alta consistencia nun marco de referencia ALE. Ademais, o procedemento seguido para obter a forma semi-discreta realiza o seguimento dun termo na fronteira que facilita a implementación das condicións de contorno. Outra importante contribución relacionase co concepto xeral da formulación MLSPHALE proposta. Demostrase que o esquema MLSPH-ALE é unha formulación sen malla global que con certas configuración particulares rende as mesmas formas semi-discretas que outras formulacións publicadas. O método MLSPH-ALE foi posto a proba fronte o cálculo de fluxos turbulentos. A baixa disipación implícita aportada polo solver de Riemann fai que o esquema sexa apto para acometer o modelado da turbulencia cos modelos implícitos LES. A formulación proposta captura a cascada de enerxía no rango de réxime subsónico, onde os métodos tradicionais SPH presentan deficiencias.This work has been partially supported by the Ministerio de Ciencia, Innovación y Universidades (RTI2018-093366-B-100) of the Spanish Government and by the Consellería de Educación e Ordenación Universitaria of the Xunta de Galicia, cofinanced with FEDER funds and the Universidade da Coruña