FISH: A 3D parallel MHD code for astrophysical applications

FISH is a fast and simple ideal magneto-hydrodynamics code that scales to ~10 000 processes for a Cartesian computational domain of ~1000^3 cells. The simplicity of FISH has been achieved by the rigorous application of the operator splitting technique, while second order accuracy is maintained by the symmetric ordering of the operators. Between directional sweeps, the three-dimensional data is rotated in memory so that the sweep is always performed in a cache-efficient way along the direction of contiguous memory. Hence, the code only requires a one-dimensional description of the conservation equations to be solved. This approach also enable an elegant novel parallelisation of the code that is based on persistent communications with MPI for cubic domain decomposition on machines with distributed memory. This scheme is then combined with an additional OpenMP parallelisation of different sweeps that can take advantage of clusters of shared memory. We document the detailed implementation of a second order TVD advection scheme based on flux reconstruction. The magnetic fields are evolved by a constrained transport scheme. We show that the subtraction of a simple estimate of the hydrostatic gradient from the total gradients can significantly reduce the dissipation of the advection scheme in simulations of gravitationally bound hydrostatic objects. Through its simplicity and efficiency, FISH is as well-suited for hydrodynamics classes as for large-scale astrophysical simulations on high-performance computer clusters. In preparation for the release of a public version, we demonstrate the performance of FISH in a suite of astrophysically orientated test cases.Comment: 27 pages, 11 figure

Kinetische Methoden zur numerischen Simulation von nichtlinearen Strömungen mit freien Oberflächen im Bau- und Umweltingenieurwesen

This thesis focuses on the numerical simulation of non-linear free surface flow problems. Different simulation kernels based on the Lattice Boltzmann method (LBM) have been developed or extended, implemented, and, after validation, applied to a number of applications in civil and environmental engineering. The LB model solves viscous and turbulent flows, essentially representing similar physics as Navier-Stokes or reduced shallow water models, but with specific solver advantages concerning data locality and parallel computing. The first part of this thesis deals with numerical simulations on high-performance GPU (graphics processing unit) hardware. Validations and applications of a reduced LB model for solving the shallow water equations are presented. The resulting GPU kernel has shown to be applicable to state-of-the-art benchmark problems, dealing with wave propagation and wave run-up. Subsequently, the GPU implementation of a 3D numerical wave tank for the simulation of various applications in civil engineering is presented. The second main target of this thesis is to develop and apply a novel model based on an enhanced representation and advection of the phase interface for the simulation of more complex and demanding free surface flow problems. A volume-of-fluid (VOF) approach in combination with a piecewise linear interface reconstruction (PLIC) has been coupled with the LBM. The resulting hybrid model has been successfully validated against various benchmark experiments. Even a breaking wave during shoaling on a slope, which is a demanding test case for VOF solvers, was successfully simulated. Apart from the model development and validation itself, a coupling to a rigid body engine for the simulation of FSI problems has been established. Finally, several techniques for the coupling to a potential flow solver are discussed and validated, in order to generate realistic wave profiles and for the efficient simulation of wave run-up and wave breaking.Die vorliegende Dissertation behandelt die numerische Simulation von nichtlinearen Strömungen mit freien Oberflächen. Dazu werden verschiedene Simulationskerne auf Basis der Gitter-Boltzmann-Methode (LBM) entwickelt, implementiert und nach ihrer Validierung auf zahlreiche Aufgabenstellungen im Bau- und Umweltingenieurwesen angewendet. Die LB-Methode wird verwendet, um viskose und turbulente Strömungen numerisch zu simulieren und bietet im Vergleich zu konventionellen Lösern deutliche Vorteile bezüglich Datenlokalität und parallelem Rechnen. Der erste Teil der Arbeit beschäftigt sich mit der Simulation von Strömungsproblemen auf High-Performance-GPU (Graphics Processing Unit) Hardware. Einleitend wird die Validierung und Anwendung eines LB-Modells für Flachwassergleichungen dargestellt. Im Anschluss wird eine GPU-Implementierung eines dreidimensionalen numerischen Wellenkanals für die Simulation turbulenter Wehrströmungen, Dammbruchszenarien, des Wellenschlages auf Pfahlbauwerke und anderer Anwendungen im Bauingenieurwesen präsentiert. Das zweite Ziel dieser Arbeit ist die Entwicklung und Anwendung eines neuartigen Modells für die Simulation von komplexeren Problemen mit freier Oberfläche unter Zuhilfenahme einer erweiterten Repräsentation der Phasengrenzfläche. Ein Volume-of-Fluid (VOF) Ansatz auf der Grundlage einer abschnittsweise linearen Interface-Rekonstruktion (PLIC) wird an die LBM gekoppelt. Das resultierende hybride Modell wird anhand verschiedener Benchmarks erfolgreich validiert. Im Anschluss wird eine Kopplung an einen Starrkörper-Löser realisiert, welche die Simulation von Problemstellungen aus dem Bereich der Fluid-Struktur-Interaktion ermöglicht. Abschließend werden Techniken zur Kopplung des hybriden Lösers an einen numerischen Wellenkanal auf Basis der Potentialströmungstheorie diskutiert und validiert, die die Erzeugung realistischer Wellenprofile und die effiziente Simulation von Wellenauflauf sowie Wellenbrechen ermöglichen

Lectures on Computational Numerical Analysis of Partial Differential Equations

From Chapter 1: The purpose of these lectures is to present a set of straightforward numerical methods with applicability to essentially any problem associated with a partial differential equation (PDE) or system of PDEs independent of type, spatial dimension or form of nonlinearity.https://uknowledge.uky.edu/me_textbooks/1002/thumbnail.jp

Lectures in Computational Fluid Dynamics of Incompressible Flow: Mathematics, Algorithms and Implementations

From Prologue: The present lecture notes are written to emphasize the mathematics of the Navier–Stokes (N.–S.) equations of incompressible flow and the algorithms that have been developed over the past 30 years for solving them.https://uknowledge.uky.edu/me_textbooks/1003/thumbnail.jp

Sensitivity of VOF simulations of the liquid jet breakup to physical and numerical parameters

AbstractIn this paper the characteristics of the primary breakup of a liquid jet is analyzed numerically. We applied the Volumes of Fluids (VOF) approach utilizing the Direction Averaged Curvature (DAC) model, to estimate the interface curvature, and the Direction Averaged Normal (DAN) model, to propagate the interface. While being used for the first time to predict liquid atomization, this methodology showed a high accuracy. The influence of varying the fluid properties, namely liquid-gas density and viscosity ratio, and injection conditions is discussed related to the required grid resolution. Resulting droplet sizes are compared to distributions obtained through the One-Dimensional Turbulence (ODT) model

Perspective on the muon-spin rotation/relaxation under hydrostatic pressure

Pressure, together with temperature, electric and magnetic fields, alters the system and allows to investigate the fundamental properties of the matter. Under applied pressure the interatomic distances shrink, which modify interactions between atoms and may lead to appearance of a new (sometime exotic) physical properties as, e.g., pressure induced phase transition(s); quantum critical points(s), new structural, magnetic and/or superconducting states; changes of the temperature evolution and the symmetry of the order parameter(s) etc. The muon-spin rotation/relaxation ($\mu$SR) appears to be a commonly used powerful technique allowing to study the magnetic and superconducting responses of various materials under extreme conditions. At present, $\mu$SR experiments might be performed under the high magnetic field up to $\simeq 9$ T, temperatures down to $\simeq 10-15$ mK and hydrostatic pressure up to $\simeq 2.8$ GPa. In the following Perspective paper the requirements to the $\mu$SR under pressure experiments, the existing high-pressure muon facility at the Paul Scherrer Institute (Switzerland), and selected experimental results obtained by using the $\mu$SR under pressure technique are discussed.Comment: 14 pages, 14 figure