PoisFFT - A Free Parallel Fast Poisson Solver

A fast Poisson solver software package PoisFFT is presented. It is available as a free software licensed under the GNU GPL license version 3. The package uses the fast Fourier transform to directly solve the Poisson equation on a uniform orthogonal grid. It can solve the pseudo-spectral approximation and the second order finite difference approximation of the continuous solution. The paper reviews the mathematical methods for the fast Poisson solver and discusses the software implementation and parallelization. The use of PoisFFT in an incompressible flow solver is also demonstrated

A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods

For simulating incompressible flows by projection methods. it is generally accepted that the pressure-correction stage is the most time-consuming part of the flow solver. The objective of the present work is to develop a fast hybrid pressure-correction algorithm for numerical simulation of incompressible flows around obstacles in the context of projection methods. The key idea is to adopt different numerical methods/discretizations in the sub-steps of projection methods. Here, a classical second-order time-marching projection method which consists of two sub-steps is chosen for the purpose of demonstration. In the first sub-step, the momentum equations are discretized on unstructured grids and solved by conventional numerical methods, here, a meshless method. In the second sub-step (pressure-correction), the proposed algorithm adopts a double discretization system and combines the weighted least squares approximation with the essence of immersed boundary methods. Such a design allows us to develop a FFT-based solver to speed up the solution of the pressure Poisson equation for flow cases with obstacles, while keeping the implementation of boundary conditions for the momentum equations as easy as conventional numerical methods do with unstructured grids. Numerical experiments of five test cases have been performed to verify and validate the proposed hybrid algorithm and evaluate its computational performance. The results show that the new FFT-based hybrid algorithm is working and robust, and it is significantly faster than the multigrid-based reference method. The hybrid algorithm opens an avenue for the development of next-generation high-performance parallel computational fluid dynamics solvers for incompressible flows

Deterministic-Kinetic Computational Analyses of Expansion Flows and Current-Carrying Plasmas

Spacecraft electric propulsion (EP) takes advantage of the ability of electric and magnetic fields to accelerate plasmas to high velocities to generate efficient thrust. The thermionic hollow cathode is a critical component to both gridded-ion and Hall-effect thrusters, the state-of-the-art devices of the EP discipline. However, experiments demonstrate that the hollow cathode is plagued by erosion of its surfaces by the plasma, which may eventually cause premature failure of the device. This erosion has been linked to the ion-acoustic instability (IAI), a kinetic plasma instability which operates in the cathode plume. Existence of this kinetic instability has prevented numerical simulation from predicting the operating characteristics and lifetime of the hollow cathode device. Therefore, this thesis utilizes deterministic-kinetic (DK) simulation of gas and plasma flows to further the understanding of the IAI as it relates to the hollow cathode plume and to ultimately develop a predictive hollow cathode simulation platform. Towards these goals, two approaches to applying the DK simulation method to the hollow cathode plasma are undertaken: hybrid-kinetic simulation and fully-kinetic simulation. Hybrid-kinetic simulations utilize a kinetic description of the heavy propellant particles while using a reduced-order, fluid approach for the light electrons. Two unique two-dimensional, axisymmetric kinetic schemes are developed, one for neutral particles and one for ions; the schemes are verified by comparison with solutions obtained using the direct-simulation Monte Carlo method and with an analytic solution for a rarefied neutral jet flow. Assuming quasi-neutrality in the hollow cathode plasma and using the Boltzmann relation for the plasma potential, the hybrid-kinetic solver is applied to the problem of NASA's NSTAR discharge hollow cathode. Partial validation is achieved through agreement with experimental Langmuir probe data in the near-orifice region, while shortcomings of the solver such as use of a simplified electron model are discussed. Fully-kinetic simulations, where all species are considered kinetically, are carried out to study the IAI. The anomalous resistivity generated by the IAI is measured from one-dimensional fully-kinetic simulations and compared with a closure model commonly used in hollow cathode fluid codes, finding that the agreement with the closure model varies based on simulation domain size and electron Mach number. Further, the formation of high-energy tails in the ion velocity distribution function is observed near the transition to the Buneman instability, another instability of current-carrying plasmas. Two-dimensional kinetic simulations of current-carrying instabilities are carried out, finding that the nature of nonlinear saturation of the IAI differs significantly from that shown in one-dimensional simulations. A phenomenon known as the off-axis instability generates waves propagating normal to the current direction which eventually reach energy levels close to that of the waves along the current direction. Further fully-kinetic simulations demonstrate the formation of weak plasma double layers, regions of plasma which sustain a potential gradient, in the nonlinear saturation stage of the IAI. These double layers are found to be ubiquitous in all plasma species considered, even the heavy xenon ions commonly used in hollow cathodes. Phase space analysis suggests the double layers form from ion-acoustic wave packets which grow into ion phase space holes. Spectral analysis demonstrates a shift towards smaller wavenumbers which marks this transition. An electron two-stream instability is spawned due to the potential well of the double layer, where spectral analyses demonstrate that a simple theoretical expression well-predicts the resulting wave phase velocity.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169806/1/vazsonyi_1.pd

Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh–Bénard convection

We present the adaptation to non–free boundary conditions of a pseudospectral method based on the (complex) Fourier transform. The method is applied to the numerical integration of the Oberbeck–Boussinesq equations in a Rayleigh–Bénard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number (R ∼ 10^9). These results are the basis for the later study, by the same method, of wet convection in a solar still.publishedVersionFil: Ramos, Ivana Carola. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Briozzo, Carlos Bruno. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Física de los Fluidos y Plasm

Efficient algorithms for the fast computation of space charge effects caused by charged particles in particle accelerators

In this dissertation, a Poisson solver is improved with three parts: the efficient integrated Green's function; the discrete cosine transform of the efficient integrated Green's function values; the implicitly zero-padded fast Fourier transform for charge density. In addition, the high performance computing technology is utilized for the further improvement of efficiency, such as: OpenMP API, OpenMP+CUDA, MPI, and MPI+OpenMP parallelizations. The examples and simulation results are matched with the results of the commonly used Poisson solver to demonstrate the accuracy performance

Resolución eficiente de la ecuación de Poisson en un clúster de GPU

176 p.Este trabajo de investigación se enmarca en el contexto de la computación de alto rendimiento(High Performance Computing, HPC) y, más en concreto, en la computación paralela utilizandocomputación de propósito general en GPU (General-Purpose computing on GPU, GPGPU). Aunqueel trabajo surge en el contexto de la física computacional, las aportaciones de esta tesis sonaplicables a múltiples ámbitos de la vida real: electrostática, ingeniería mecánica, etc.El objetivo principal de este trabajo se ha centrado en la resolución eficiente de la ecuación dePoisson en un clúster de unidades de procesamiento gráfico (Graphics Processing Units, GPU) y sehan aplicado diversas técnicas con el fin de optimizar los programas implementados: técnicas desegmentación software, optimización del acceso a memoria, sincronización, estimación deparámetros óptimos de las librerías de cómputo, etc

Modelización y simulación numérica de un destilador solar

Tesis (Doctor en Física)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física, 2015.En esta tesis se desarrolla un modelo termohidrodinámico de un destilador solar de batea. Inicialmente, mediante descomposición en modos empíricos y transformada de Hilbert-Huang, se realiza un reanálisis de resultados experimentales previos obtenidos con un modelo de laboratorio en la Universidad Nacional de Salta. A continuación se desarrolla un modelo termodinámico para aire húmedo sub y sobresaturado, incluyendo la transición de fase líquido-vapor. A partir de este modelo se formula un modelo hidrodinámico, en la aproximación de Boussinesq que describe el transporte de energía, momento y concentración de agua dentro del destilador. Para su integración numérica se desarrolla un método pseudoespectral basado en transformada de Fourier, adaptándolo a la condiciones de contorno y geometría del destilador. Se realizan simulaciones numéricas correspondientes al régimen de funcionamiento del modelo de laboratorio en una de sus dos configuraciones geométricas, lográndose reproducir la fenomenología observada y los resultados experimentales de flujo térmico y rendimiento de agua destilada con buena precisión. Estos resultados indican que el modelo tiene poder predictivo y podrá ser utilizado para estudiar modificaciones de diseño destinadas a maximizar el rendimiento del destilador