MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Drift instabilities, anomalous transport, and heating in low-temperature plasmas

Plasma is an ideal gas of charged particles (ions and electrons) in addition to neutral particles. The presence of charged particles results in the generation of electric and magnetic fields that serve as the primary mechanism of the interaction and coupling of particles. As a result, various nonlinear collective phenomena occur in the plasma, the understanding of many of which remains elusive today. On the other hand, plasmas have many applications in different branches of science and technology. Different kinds of plasmas are studied in the atmospheric and space sciences. In the semiconductor industry, the fabrication of electronic chips relies heavily on plasma etching. Plasma is used in modern electrical thrusters for producing the driving force of satellites and spacecrafts. It is also used in future fusion reactors for producing abundant clean energy. Therefore, understanding the complicated phenomena in plasma is important for predicting and controlling its behaviours in various conditions. In this regard, nonlinear phenomena, such as turbulence, are formidable barriers to understanding plasma behaviours. These phenomena are described by nonlinear differential equations that can be barely understood by analytical means and are usually investigated by numerical simulations. Because of this, it is also important to understand the effect of numerical artifacts on simulations. In this thesis, we investigate the nonlinear characteristics of drift instabilities and the role of numerical methods in our understanding of these instabilities. The drift instabilities are driven by excess free energy that exists due to the average (drift) velocities of electron and ion components in plasmas. As a result of these instabilities, the amplitude of fluctuations grows while the drift energy converts into electrostatic energy. This growth continues until the nonlinear effects, such as turbulence, trapping, and wave-wave interactions, become active. As a result of these nonlinear effects, the growth of the fluctuations saturates. In this thesis, our focus will be on two particular types of drift instabilities, namely the Buneman instability and electron-cyclotron drift instability (ECDI). The Buneman instability is driven when a beam of electrons is injected into the stationary ions, while both electrons and ions are unmagnetized. In the ECDI, however, the electrons are magnetized and are also influenced by an external electric field, perpendicular to the magnetic field. This configuration of fields leads to the E × B drift of the electrons that drives the ECDI. Many kinetic simulations are performed, and several nonlinear phenomena such as trapping, heating, anomalous transport, backward waves, and transition of magnetized plasmas to the unmagnetized regime are studied with regard to both instabilities. For the study of the nonlinear effects of drift instabilities, a grid-based Vlasov code is developed and used. The numerical method used in this code is the “semi-Lagrangian” method, which is among the most popular methods for continuum simulations of plasma. In the study of the drift instabilities, we compare the results of the semi-Lagrangian Vlasov simulations with the more traditional particle-in-cell (PIC) method. The results of these benchmarking studies reveal several similarities and discrepancies between Vlasov and particle-in-cell simulations, showing how the numerical methods can interfere with the physics of the problems

Real-Time Simulation of Indoor Air Flow using the Lattice Boltzmann Method on Graphics Processing Unit

This thesis investigates the usability of the lattice Boltzmann method (LBM) for the simulation of indoor air flows in real-time. It describes the work undertaken during the three years of a Ph.D. study in the School of Mechanical Engineering at the University of Leeds, England. Real-time fluid simulation, i.e. the ability to simulate a virtual system as fast as the real system would evolve, can benefit to many engineering application such as the optimisation of the ventilation system design in data centres or the simulation of pollutant transport in hospitals. And although real-time fluid simulation is an active field of research in computer graphics, these are generally focused on creating visually appealing animation rather than aiming for physical accuracy. The approach taken for this thesis is different as it starts from a physics based model, the lattice Boltzmann method, and takes advantage of the computational power of a graphics processing unit (GPU) to achieve real-time compute capability while maintaining good physical accuracy. The lattice Boltzmann method is reviewed and detailed references are given a variety of models. Particular attention is given to turbulence modelling using the Smagorinsky model in LBM for the simulation of high Reynolds number flow and the coupling of two LBM simulations to simulate thermal flows under the Boussinesq approximation. A detailed analysis of the implementation of the LBM on GPU is conducted. A special attention is given to the optimisation of the algorithm, and the program kernel is shown to achieve a performance of up to 1.5 billion lattice node updates per second, which is found to be sufficient for coarse real-time simulations. Additionally, a review of the real-time visualisation integrated within the program is presented and some of the techniques for automated code generation are introduced. The resulting software is validated against benchmark flows, using their analytical solutions whenever possible, or against other simulation results obtained using accepted method from classical computational fluid dynamics (CFD) either as published in the literature or simulated in-house. The LBM is shown to resolve the flow with similar accuracy and in less time