Numerično modeliranje dendritskega strjevanja na podlagi formulacije faznega polja in prilagodljivega brezmrežnega rešitvenega postopka

The main aim of the dissertation is to develop a novel numerical approach for an accurate and computationally efficient modelling of dendritic solidification, which is one of the most commonly observed phenomena in the industrial casting of the metallic alloys. The size and the morphology of dendritic structures as well as the distribution of the solute within them critically effect the mechanical and the electro-chemical properties of the solidified material. The numerical modelling of dendritic solidification can be applied for an in-depth understanding and optimisation of the casting process under various solidification conditions and chemical compositions of the alloy under consideration. The dendritic solidification of pure materials and dilute multi-component alloys is considered in the dissertation. The phase field formulation is applied for the modelling of dendritic solidification. The formulation is based on the introduction of the continuous phase field variable that is constant in the bulk of the solid and liquid phases. The phase field variable has a smooth transition from the value denoting the solid phase to the value denoting the liquid phase at the solid-liquid interface over the characteristic interface thickness. A phase field model yields a system of coupled non-linear parabolic partial differential equations that govern the evolution of the phase field and other thermodynamic variables. The meshless radial basis function-generated finite-differences (RBF-FD) method is used for the spatial discretisation of the system of partial differential equations. The forward Euler scheme is applied for the temporal discretisation. Fifth-degree polyharmonic splines are used as the shape functions in the RBF-FD method. A second-order accurate RBF-FD method is achieved by augmenting the shape functions with monomials up to the second degree. The adaptive solution procedure is developed in order to speed-up the calculations. The procedure is based on the quadtree domain decomposition of a rectangular computational domain into rectangular computational sub-domains of different sizes. Each quadtree sub-domain has its own regular or scattered distribution of computational nodes in which the RBF-FD method and the forward Euler scheme apply for the discretisation of the system of partial differential equations. The adaptive solution procedure dynamically ensures the prescribed highest density of the computational nodes at the solid-liquid interface and the lowest-possible density in the bulk of the solid and liquid phases. The adaptive time-stepping is employed to further speed-up the calculations. The stable time step in the forward Euler scheme depends on the density of the computational nodeshence, different time steps can be used in quadtree sub-domains with different node densities. The main originality of the present work is the use of the RBF-FD method for the thorough analysis of the impact of the type of the node distribution and the size of a local sub-domain to the accuracy when the phase field modelling of dendritic solidification for arbitrary preferential growth directions is considered. It is shown how the use of the scattered node distribution reduces the undesirable mesh-induced anisotropy effects, present when the partial differential equations are discretisied on a regular node distribution. The main advantage of the RBF-FD method for the phase field modelling of dendritic growth is the simple discretisation of the partial differential equations on the scattered node distributions. The RBF-FD method is, for the first time, used in combination with the spatial-temporal adaptive solution procedure based on the quadtree domain decomposition. The adaptive solution procedure successfully speeds-up the calculationshowever, the advantages of the use of the scattered node distribution are partly compromised due to the impact of regularity in the quadtree domain decomposition.Glavni cilj disertacije je razvoj novega numeričnega pristopa za natančno in računsko učinkovito modeliranje dendritskega strjevanja. Dendritsko strjevanje je eden najpogosteje opaženih pojavov pri industrijskem ulivanju kovinskih zlitin. Velikost in morfologija dendritskih struktur ter porazdelitev topljencev v njih ključno vplivajo na mehanske in elektro-kemijske lastnosti strjenega materiala. Numerično modeliranje dendritskega strjevanja se lahko uporablja za poglobljeno razumevanje in optimizacijo procesa ulivanja pri različnih pogojih strjevanja in pri različnih kemijskih sestavah obravnavane zlitine. V disertaciji obravnavamo dendritsko strjevanje čistih snovi in razredčenih več-sestavinskih zlitin. Za modeliranje dendritskega strjevanja uporabimo formulacija faznega polja. Formulacija temelji na uvedbi zvezne spremenljivke faznega polja, ki je konstantna v trdni in kapljeviti fazi. Spremenljivka faznega polja ima na medfaznem robu zvezen prehod preko značilne debeline medfaznega roba od vrednosti, ki označuje trdno fazo, do vrednosti, ki označuje kapljevito fazo. Model faznega polja poda sistem sklopljenih nelinearnih paraboličnih parcialnih diferencialnih enačb, ki opisujejo časovni razvoj faznega polja in ostalih termodinamskih spremenljivk. Za krajevno diskretizacijo sistema parcialnih diferencialnih enačb uporabimo brezmrežno metodo z radialnimi baznimi funkcijami generiranih končnih razlik (RBF-KR). Za časovno diskretizacijo uporabimo eksplicitno Eulerjevo shemo. Poliharmonične zlepke petega reda uporabimo kot oblikovne funkcije v metodi RBF-KR. Natančnost drugega reda metode RBF-KR dosežemo z dodajanjem monomov do vključno drugega reda k oblikovnim funkcijam. Za pospešitev izračunov razvijemo prilagodljiv rešitveni postopek. Postopek temelji na razdelitvi pravokotne računske domene na pravokotne računske pod-domene različnih velikosti z uporabo štiriškega drevesa. Vsaka pod-domena na štiriškem drevesu vsebuje svojo lastno regularno ali razmetano porazdelitev računskih točk, v katerih z uporabo metode RBF-KR in eksplicitne Eulerjeve sheme diskretiziramo sistem parcialnih diferencialnih enačb. Prilagodljiv rešitveni postopek dinamično zagotavlja predpisano najvišjo gostoto računskih točk na trdno-kapljevitem medfaznem robu in najmanjšo možno gostoto v notranjosti trdne in kapljevite faze. Za dodatno pohitritev izračunov uporabimo prilagodljivo časovno korakanje. Stabilen časovni korak v eksplicitni Eulerjevi shemi je odvisen od gostote računskih točk, zaradi česar lahko uporabimo različne časovne korake v pod-domenah štiriškega drevesa z različnimi gostotami točk. Glavna novost predstavljenega dela je v uporabi metode RBF-KR za temeljito analizo vpliva tipa porazdelitve računskih točk in velikosti lokalnih pod-domen na natančnost pri modeliranju dendritskega strjevanja pri poljubnih preferenčnih smereh rasti z uporabo metode faznega polja. Pokažemo, kako uporaba razmetanih računskih točk zmanjša neželjen vpliv mrežne anizotropije, ki je prisotna, kadar parcialne diferencialne enačbe diskretiziramo na regularni porazdelitvi računskih točk. Glavna prednost metode RBF-KR za modeliranje dendritskega strjevanja je preprosta diskretizacija parcialnih diferencialnih enačb na razmetanih porazdelitvah računskih točk. Metoda RBF-KR je prvič uporabljena v kombinaciji s krajevno-časovnim prilagodljivim rešitvenim postopkom, ki temelji na razdelitvi računske domene s štiriškim drevesom. Prilagodljiv rešitveni postopek uspešno pohitri izračune, vendar se prednosti uporabe razmetane porazdelitve računskih točk delno zmanjšajo zaradi vpliva regularnosti pri razdelitvi računske domene s štiriškim drevesom

Developments of numerical methods for linear and nonlinear fluid-solid interaction dynamics with applications

This paper presents a review on some developments of numerical methods for linear and nonlinear fluid-solid interaction (FSI) problems with their applications in engineering. The discussion covers the four types of numerical methods: 1) mixed finite element (FE)-substructure-subdomain model to deal with linear FSI in a finite domain, such as sloshing, acoustic-structure interactions, pressure waves in fluids, earthquake responses of chemical vessels, dam-water couplings, etc.; 2) mixed FE-boundary element (BE) model to solve linear FSI with infinite domains, for example, VLFS subject to airplane landing impacts, ship dynamic response caused by cannon / missile fire impacts, etc.; 3) mixed FE-finite difference (FD) / volume (FV) model for nonlinear FSI problems with no separations between fluids and solids and breaking waves; 4) mixed FE-smooth particle (SP) method to simulate nonlinear FSI problems with f-s separations as well as breaking waves. The partitioned iteration approach is suggested in base of available fluid and solid codes to separately solve their governing equations in a time step, and then through reaching its convergence in coupling iteration to forward until the problem solved. The selected application examples include air-liquid-shell three phases interactions, LNG ship-water sloshing; acoustic analysis of air-building interaction system excited by human foot impacts; transient dynamic response of an airplane-VLFS-water interaction system excited by airplane landing impacts; turbulence flow-body interactions; structure dropping down on the water surface with breaking waves, etc. The numerical results are compared with the available experiment or numerical data to demonstrate the accuracy of the discussed approaches and their values for engineering applications. Based on FSI analysis, linear and nonlinear wave energy harvesting devices are listed to use the resonance in a linear system and the periodical solution in a nonlinear system, such as flutter, to effectively harvest wave energy. There are 231 references are given in the paper, which provides very useful resources for readers to further investigate their interesting approaches

B-spline based Boundary Method for the Material Point Method

Unlike the conventional finite element method, in which the mesh conforms to the material boundary, the material point method (MPM) does not provide a clear interpretation of the boundary. Consequently, difficulties arise when it comes to solving boundary-value problems during MPM simulations, in particular, applying traction (Neumann) and prescribed displacement (inhomogeneous Dirichlet) boundary conditions. However, little attention has been paid to this issue; no literature to date has presented an effective way to model and track boundaries in the MPM. Hence, developing new ways of boundary representation and boundary conditions application in the MPM is the focus of this research. Formulation of the MPM is firstly presented followed by a review on current approaches to this boundary issue, where B-spline interpolation techniques and an implicit boundary method are identified as the methods to be taken forward. Essential knowledge on B-splines is then discussed. After comparing different B-spline interpolation techniques, a local cubic scheme is selected for boundary representation due to its ability to handle sharp corners and its relatively high computational stability. Next, enforcements of the boundary conditions are discussed. Tractions are applied through direct integration over the B-spline boundary and displacements are prescribed via a B-spline based implicit boundary method. Finally, this boundary method is verified through numerical examples, several of which were not possible with previous MPMs. The novelty of this thesis lies in providing a complete methodology on modelling and tracking the boundaries as well as accurately imposing both Neumann and Dirichlet boundary conditions in the MPM

Modelling of defects in aluminium cast products

Over the last 4 decades, remarkable progress has been made in the modelling of casting processes. The development of casting models is well reflected in the proceedings of the 15 Modelling of Casting, Welding and Advanced Solidification Processes (MCWASP) conferences that have been held since 1980. Computer simulations have enabled a better understanding of the physical phenomena involved during solidification. Modelling gives the opportunity to uncouple the physical processes. Furthermore, quantities that are difficult or impossible to measure experimentally can be calculated using computer simulations e.g. flow patterns and recalescence. However, when it comes to accurately predicting casting performance and in particular, the occurrence of defects like cracks, segregation and porosity there is certainly some way to go. In this paper, the current understanding of the main mechanisms of defect formation during shape and DC casting processes will be reviewed and requirements will be discussed to give a direction to making casting models more predictive and quantitative

Development and applications of the Finite Point Method to compressible aerodynamics problems

This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems. The research focuses mainly on investigating the capabilities of the meshless technique to address practical problems, one of the most outstanding issues in meshless methods. The FPM spatial approximation is studied firstly, with emphasis on aspects of the methodology that can be improved to increase its robustness and accuracy. Suitable ranges for setting the relevant approximation parameters and the performance likely to be attained in practice are determined. An automatic procedure to adjust the approximation parameters is also proposed to simplify the application of the method, reducing problem- and user-dependence without affecting the flexibility of the meshless technique. The discretization of the flow equations is carried out following wellestablished approaches, but drawing on the meshless character of the methodology. In order to meet the requirements of practical applications, the procedures are designed and implemented placing emphasis on robustness and efficiency (a simplification of the basic FPM technique is proposed to this end). The flow solver is based on an upwind spatial discretization of the convective fluxes (using the approximate Riemann solver of Roe) and an explicit time integration scheme. Two additional artificial diffusion schemes are also proposed to suit those cases of study in which computational cost is a major concern. The performance of the flow solver is evaluated in order to determine the potential of the meshless approach. The accuracy, computational cost and parallel scalability of the method are studied in comparison with a conventional FEM-based technique. Finally, practical applications and extensions of the flow solution scheme are presented. The examples provided are intended not only to show the capabilities of the FPM, but also to exploit meshless advantages. Automatic hadaptive procedures, moving domain and fluid-structure interaction problems, as well as a preliminary approach to solve high-Reynolds viscous flows, are a sample of the topics explored. All in all, the results obtained are satisfactorily accurate and competitive in terms of computational cost (if compared with a similar mesh-based implementation). This indicates that meshless advantages can be exploited with efficiency and constitutes a good starting point towards more challenging applications.En este trabajo se aborda el desarrollo del Método de Puntos Finitos (MPF) y su aplicación a problemas de aerodinámica de flujos compresibles. El objetivo principal es investigar el potencial de la técnica sin malla para la solución de problemas prácticos, lo cual constituye una de las limitaciones más importantes de los métodos sin malla. En primer lugar se estudia la aproximación espacial en el MPF, haciendo hincapié en aquéllos aspectos que pueden ser mejorados para incrementar la robustez y exactitud de la metodología. Se determinan rangos adecuados para el ajuste de los parámetros de la aproximación y su comportamiento en situaciones prácticas. Se propone además un procedimiento de ajuste automático de estos parámetros a fin de simplificar la aplicación del método y reducir la dependencia de factores como el tipo de problema y la intervención del usuario, sin afectar la flexibilidad de la técnica sin malla. A continuación se aborda el esquema de solución de las ecuaciones del flujo. La discretización de las mismas se lleva a cabo siguiendo métodos estándar, pero aprovechando las características de la técnica sin malla. Con el objetivo de abordar problemas prácticos, se pone énfasis en la robustez y eficiencia de la implementación numérica (se propone además una simplificación del procedimiento de solución). El comportamiento del esquema se estudia en detalle para evaluar su potencial y se analiza su exactitud, coste computacional y escalabilidad, todo ello en comparación con un método convencional basado en Elementos Finitos. Finalmente se presentan distintas aplicaciones y extensiones de la metodología desarrollada. Los ejemplos numéricos pretenden demostrar las capacidades del método y también aprovechar las ventajas de la metodología sin malla en áreas en que la misma puede ser de especial interés. Los problemas tratados incluyen, entre otras características, el refinamiento automático de la discretización, la presencia de fronteras móviles e interacción fluido-estructura, como así también una aplicación preliminar a flujos compresibles de alto número de Reynolds. Los resultados obtenidos muestran una exactitud satisfactoria. Además, en comparación con una técnica similar basada en Elementos Finitos, demuestran ser competitivos en términos del coste computacional. Esto indica que las ventajas de la metodología sin malla pueden ser explotadas con eficiencia, lo cual constituye un buen punto de partida para el desarrollo de ulteriores aplicaciones.Postprint (published version

Development and applications of the finite point method to compressible aerodynamics problems

This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems. The research focuses mainly on investigating the capabilities of the meshless technique to address practical problems, one of the most outstanding issues in meshless methods. The FPM spatial approximation is studied firstly, with emphasis on aspects of the methodology that can be improved to increase its robustness and accuracy. Suitable ranges for setting the relevant approximation parameters and the performance likely to be attained in practice are determined. An automatic procedure to adjust the approximation parameters is also proposed to simplify the application of the method, reducing problem- and user-dependence without affecting the flexibility of the meshless technique. The discretization of the flow equations is carried out following wellestablished approaches, but drawing on the meshless character of the methodology. In order to meet the requirements of practical applications, the procedures are designed and implemented placing emphasis on robustness and efficiency (a simplification of the basic FPM technique is proposed to this end). The flow solver is based on an upwind spatial discretization of the convective fluxes (using the approximate Riemann solver of Roe) and an explicit time integration scheme. Two additional artificial diffusion schemes are also proposed to suit those cases of study in which computational cost is a major concern. The performance of the flow solver is evaluated in order to determine the potential of the meshless approach. The accuracy, computational cost and parallel scalability of the method are studied in comparison with a conventional FEM-based technique. Finally, practical applications and extensions of the flow solution scheme are presented. The examples provided are intended not only to show the capabilities of the FPM, but also to exploit meshless advantages. Automatic hadaptive procedures, moving domain and fluid-structure interaction problems, as well as a preliminary approach to solve high-Reynolds viscous flows, are a sample of the topics explored. All in all, the results obtained are satisfactorily accurate and competitive in terms of computational cost (if compared with a similar mesh-based implementation). This indicates that meshless advantages can be exploited with efficiency and constitutes a good starting point towards more challenging applications

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

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

Development of design criteria for novel 3D-printed quadric-surfaced sludge digesters for wastewater infrastructure

The quadric-surfaced sludge digester (QSD), also known as the egg-shaped sludge digester, has proven its advantages over traditional cylindrical digesters recently. A reduction in operational cost is the dominant factor. Its shell can be described as a revolution of a parabola with the apex and base being either tapered or spherical. This shape provides a surface free of discontinuities, which is advantageous regarding the efficiency during mixing. Since the shape does not produce areas of inactive fluid motion within the tank, sludge settlement and an eventual grit build-up are avoided. The stresses developed in the shell of the sludge digester, vary along the meridian and equatorial diameters. A non-dimensional parameter, ξ, defines the height-to-diameter aspect ratio which is used to delineate the parametric boundary conditions of the shell’s surface. Three groups of analyses were conducted to determine the orthogonal stresses in the shell of the QSD. The first-principles numerical models ran reasonably quickly, and many iterations were made during the study. The results showed that they were in within the range 5.34% to 7.2% to 2D FEA simulations. The 3D FEA simulations were within the range of 8.3% to 9.2% to the MATLAB time-history models. This is a good indicator that the first principles numerical models are an excellent time-saving method to predict the behaviour of the QSD under seismic excitation. Upon examining the criteria for the design, analysing the results for the 2D FEA simulations showed that the fill height is not a significant variable with sloshing however the 3D FEA showed that the hydrostatic pressure is a significant variable. With the maximum tensile stress of the 3D-printed ABS being 24.4 MPa, the overall maximum stress of 5.45 MPa, the material can be a viable option for the use of QSD construction in small island developing states (SIDS)

Improved multiphase smoothed particle hydrodynamics

Smoothed Particle Hydrodynamics (SPH) is a relatively new meshless numerical approach which has attracted significant attention in the last 15 years. Compared with the conventional mesh-dependent computational fluid dynamics (CFD) methods, the SPH approach exhibits unique advantages in modeling multiphase fluid flows and associated transport phenomena due to its capabilities of handling complex material surface behavior as well as modeling complicated physics in a relatively simple manner. On the other hand, as SPH is still a developing CFD tool, it is vital to investigate its attributes, namely, advantages or potential limitations in modeling different multiphase flow problems to further understand and then improve this technique. Toward this end, this work aims to design a computational code using SPH method for the simulation of multiphase flows. In this work, we present numerical solutions for flow over an airfoil and square obstacle using both weakly compressible and incompressible SPH method with an improved solid boundary treatment approach, referred to as Multiple Boundary Tangents (MBT) method. It is shown that the MBT boundary treatment technique is very effective for tackling boundaries of complex shapes. Also, we have proposed the usage of the repulsive component of the Leonard Jones Potential (LJP) in the advection equation to repair particle fracture occurring in SPH method due to the tendency of SPH particles to follow the stream line trajectory. This approach is named as the artificial particle displacement method. Furthermore, the proposed method is totalized for the multiphase uid systems and implemented accordingly. The presented model is validated by solving Laplace's law, and square bubble deformation without surface tension whereby it is shown that the implemented SPH discretization does not produce any artificial surface tension. Then, the problem descriptions and solutions for two important hydrodynamic instabilities namely, Kelvin-Helmholtz and Rayleigh-Taylor instabilities, are provided along with their brief analytical linear stability analysis to describe the accuracy and the limitation of the numerical scheme. The long time evolution for both cases are investigated and the comparison between the simulation results and existence theories are provided in details. Finally, we have presented a model to study the deformation of a droplet suspended in a quiescent fluid subjected to the combined effects of surface tension and electric field forces. The electrostatics phenomena are coupled to hydrodynamics through the solution of a set of Maxwell equations. The relevant Maxwell equations and associated interface conditions are simplified relying on the assumptions of the so called leaky dielectric model. All governing equations and the relevant jump and boundary conditions are discretized in space using the SPH method with improved interface and boundary treatments. Numerical results are validated by two highly credential analytical results which are frequently cited in the literature