Towards better understanding of the Smoothed Particle Hydrodynamic Method

Numerous approaches have been proposed for solving partial differential equations; all these methods have their own advantages and disadvantages depending on the problems being treated. In recent years there has been much development of particle methods for mechanical problems. Among these are the Smoothed Particle Hydrodynamics (SPH), Reproducing Kernel Particle Method (RKPM), Element Free Galerkin (EFG) and Moving Least Squares (MLS) methods. This development is motivated by the extension of their applications to mechanical and engineering problems. Since numerical experiments are one of the basic tools used in computational mechanics, in physics, in biology etc, a robust spatial discretization would be a significant contribution towards solutions of a number of problems. Even a well-defined stable and convergent formulation of a continuous model does not guarantee a perfect numerical solution to the problem under investigation. Particle methods especially SPH and RKPM have advantages over meshed methods for problems, in which large distortions and high discontinuities occur, such as high velocity impact, fragmentation, hydrodynamic ram. These methods are also convenient for open problems. Recently, SPH and its family have grown into a successful simulation tools and the extension of these methods to initial boundary value problems requires further research in numerical fields. In this thesis, several problem areas of the SPH formulation were examined. Firstly, a new approach based on ‘Hamilton’s variational principle’ is used to derive the equations of motion in the SPH form. Secondly, the application of a complex Von Neumann analysis to SPH method reveals the existence of a number of physical mechanisms accountable for the stability of the method. Finally, the notion of the amplification matrix is used to detect how numerical errors propagate permits the identification of the mechanisms responsible for the delimitation of the domain of numerical stability. By doing so, we were able to erect a link between the physics and the numerics that govern the SPH formulation.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Smoothed Particle Hydrodynamics for Computational Fluid Dynamics

Smoothed particle hydrodynamics (SPH) is a simple and effective numerical method that can be used to solve a variety of challenging problems in computational mechanics. It is a Lagrangian mesh-free method ideal for solving deformation problems. In the SPH method, the state of a system is represented by a set of particles, which possesses individual material properties and interact with each other within a specific range defined as a support domain by a weight function or smoothing function. SPH features flexibility in handling complex flow fields and in including physical effects. In theory, the basic concept of the SPH method is introduced in this paper. Some detailed numerical aspects are discussed including the kernel approximation in continuous form and particle approximation in discrete form, the properties for the smoothing functions and some of the most frequently used ones in the SPH literature, the concept of support and interface domain, SPH formulations for Navier-Stokes equation, time integration, boundary treatment, particle interaction, artificial viscosity, laminar viscosity, shifting algorithm, and so on. In applications, this paper presents an improved SPH method for modeling the diffusion process of a microneedle and using smoothed particle hydrodynamics (SPH) method to simulate the 25% cross-section stenosis blood vessel model and the 75% crosssection stenosis blood vessel model. The obtained numerical results are in close agreement with available theoretical and experimental results in the literature. As an emerging transdermal drug delivery device, microneedles demonstrate some superior potential and advantages over traditional metallic needles-on-syringes in skin injection and vaccine [1]. However, very few research papers are available. This project uses a high order continuous method, the spectral element method (SEM), and a low order discrete method, the Smoothed Particle Hydrodynamics (SPH), to investigate this new drug delivery system. The incompressible Navier-Stokes equations were solved with SEM under appropriate initial and slip boundary conditions for the transport of medicine inside microneedles of rectangular and circular cross-sections. In addition, Darcy-Brinkman equations and a concentration equation were solved with SEM under appropriate initial and boundary conditions for the infiltration of medicine solution through porous media of the dermis tissue once a microneedle enters the skin. Meanwhile, the Lagrangian form of the Navier-Stokes equations were solved with the weighted interpolation approach via numerical integrations without inverting any matrices. Results from the mesh-based SEM and the mesh-free SPH simulations revealed technical details about the processes of delivery of medicine particles through microneedles and diffusion in the skin tissue, and the medicine concentration changes with space and time. The overall effect of medicine delivery under initial concentration and conditions were simulated and the effect of drug delivery were assessed. The formation of thrombus is a complicated process. The existing literature rarely has a model for high-fidelity simulation of the effects and hazards of blood clots on blood flow. In this model, high-fidelity simulations are performed for complex human internal environments. The result of this simulation indicates high pressure area in blood vessel wall which matches the real condition of the vessel experiment

Origin and Evolution of Large-scale Magnetic Fields

Magnetic elds are ubiquitous at all scales in the Universe and have been observed in galaxies and clusters of galaxies via observations of di use radio emission and Faraday Rotation Measures. Despite the observations, the origin and impact of the magnetic elds in these systems is poorly understood. In this thesis we develop a state of the art cosmological Smoothed Particle Magnetohydrodynamics code, GCMHD+, to enable the study of the magnetic elds of the largest bound structures in the Universe. Using a wide range of idealized test problems, we justify our choice of free parameters and demonstrate the performance of the code relative to analytical solutions and the results produced by a grid based MHD scheme. We then used the code to investigate the evolution of a seed magnetic eld due to the formation of structure. By varying the numerical scheme, we demonstrate that the growth of magnetic elds in galaxy clusters are very sensitive to the growth of numerical divergence of the magnetic eld. We nd that amplitude and topology of the cluster magnetic eld are insensitive to the mass or formation history of the cluster. Using high resolution simulations, we show that a primordial seed magnetic eld is capable of reproducing a wide range of observations of large-scale magnetic elds in galaxy clusters. Additionally, we examine the impact of the formation of spiral structure in a disc galaxy on the galactic magnetic eld. We nd that the numerical scheme can become unstable unless the divergence cleaning scheme is limited. We nd that the rotation of the galaxy produces a disc orientated magnetic eld with a spiral structure and large-scale eld reversals. The formation of spiral arms ampli es the ambient G magnetic eld to 20 G, in agreement with the observations of spiral galaxies. We conclude that additional physics is required to produce a more realistic galactic magnetic eld

Investigation of the use of meshfree methods for haptic thermal management of design and simulation of MEMS

This thesis presents a novel approach of using haptic sensing technology combined with virtual environment (VE) for the thermal management of Micro-Electro-Mechanical-Systems (MEMS) design. The goal is to reduce the development cycle by avoiding the costly iterative prototyping procedure. In this regard, we use haptic feedback with virtua lprototyping along with an immersing environment. We also aim to improve the productivity and capability of the designer to better grasp the phenomena operating at the micro-scale level, as well as to augment computational steering through haptic channels. To validate the concept of haptic thermal management, we have implemented a demonstrator with a user friendly interface which allows to intuitively "feel" the temperature field through our concept of haptic texturing. The temperature field in a simple MEMS component is modeled using finite element methods (FEM) or finite difference method (FDM) and the user is able to feel thermal expansion using a combination of different haptic feedback. In haptic application, the force rendering loop needs to be updated at a frequency of 1Khz in order to maintain continuity in the user perception. When using FEM or FDM for our three-dimensional model, the computational cost increases rapidly as the mesh size is reduced to ensure accuracy. Hence, it constrains the complexity of the physical model to approximate temperature or stress field solution. It would also be difficult to generate or refine the mesh in real time for CAD process. In order to circumvent the limitations due to the use of conventional mesh-based techniques and to avoid the bothersome task of generating and refining the mesh, we investigate the potential of meshfree methods in the context of our haptic application. We review and compare the different meshfree formulations against FEM mesh based technique. We have implemented the different methods for benchmarking thermal conduction and elastic problems. The main work of this thesis is to determine the relevance of the meshfree option in terms of flexibility of design and computational charge for haptic physical model

Modelling thin films and droplets using smoothed particle hydrodynamics

The small scale and length of time, in addition to the exciting phenomena (such as the inner processes within the fluid) presented by droplets and thin films, make experimen tal observations difficult and, thus require the need for computational models capable of reproducing these processes in engineering. Current computational models are dominated by Finite Element and Finite Volume methods; whilst this has advanced to a high level of improvement and understanding, they however, lack the capacity to capture large deformations adequately and applied on complex systems, which is mainly due to its dependence on their mesh requirements. The present research pro posed and developed a new method of solving thin films and droplet problems using a full Lagrangian approach known as Smoothed Particle Hydrodynamics (SPH). SPH solves the continuum set of conservation equations and provides the ability to accu rately track the fluid or material history throughout its lifetime. The thesis explores and develops new and novel single phase SPH models to reliably treat and handle the dynamic nature of surface tension effects over long simulation time scales. In particu lar, Intermolecular Interaction Force (IIF), Continuum Surface Force (CSF), Contact Line Force (CLF) and Disjoining Pressure (DP) models are developed and applied on a variety of surface tension dominated flow problems and the results, where possi ble, are validated against known analytical and experimental findings, which include investigations of droplet oscillation, wetting on substrate, contact angle hysteresis and thin film rivulet flows to highlight the capability of the proposed developed SPH methodology and models. The SPH solver is developed from scratch using C++ to maximise extensibility of the methodology and computational performance

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version