Development of a collision table for three dimensional lattice gases

Bibliography: pages 92-95.A lattice gas is a species of cellular automaton used for numerically simulating fluid flows. TransGas [9], the lattice gas code currently in use at the CSIR, is based on the FHP-I model [5], and is used to perform various two-dimensional flow simulations. In order to broaden the scope of the applications in which lattice gases can be used locally, the development of a three-dimensional lattice gas capability is required. The first major task in setting up a three dimensional-lattice gas is the construction of an efficient collision rule generator which will determine collision outcomes. For suitability to local applications, the collision rules should be chosen in such a way as to maximise the Reynolds coefficient of the flow, while conserving quantities such as mass and momentum. Part of the task thus becomes an optimisation problem. When expanding from two to three dimensions, the number of possible collision rules increases from 64 to 16777216. If a complete collision rule table is used for determining collision outcomes, storage problems are encountered on the available hardware. Selection and optimisation of collision rules cannot be done by hand when there are so many rules to choose from. Selection of rules is thus non-trivial. The work outlined in this thesis provides the CSIR with a 3-D lattice gas collision table which is well suited to the available hardware capabilities. The necessary theoretical background is considered, and a survey of the literature is presented. Based on the findings of this literature study, various methods of collision outcome determination are implemented which are considered to be suitable to the local needs, while remaining within the constraints set by hardware availability. An isometric collision algorithm, and a reduced collision table are generated and tested. A measure of the overall efficiency of a lattice gas model is determined by two factors, namely the computational efficiency and the implementation efficiency. In testing a collision table, the first is characterised by the rate at which post-collision states can be determined, and depends on the hardware and programming techniques. The second factor can be expressed by means of a number called the Reynolds coefficient, which is defined and discussed in the following chapters. The higher the Reynolds coefficient of a model, the greater the scope of flow regimes which may be simulated using it. Another advantage of having a high Reynolds coefficient is that the simulation time required for a given flow regime decreases as the Reynolds coefficient of the model increases. The overall efficiency of the isometric model is too low to be of practical use, but a significant improvement is obtained by using the method of reduced tables. In the isometric case, the number of collision outcomes that can be determined per second is similar to that of the reduced table, but the Reynolds coefficient is very much lower. Simulation of a flow regime with a Reynolds number of about 100, on a lattice of size 128³, over 20 thousand timesteps, making use of the isometric model, would take of the order of a few years to complete on the currently available hardware. Since the simulation parameters mentioned above are typical of the local requirements for lattice gas simulations, this method is obviously unsatisfactory. The isometric method does however serve as a useful introduction to three-dimensional lattice gas collision rule methods. The reduced collision table has been constructed so that it maintains semi-detailed balance, and the Boltzmann Reynolds coefficient has been calculated. In the reduced collision table model, the efficiency is higher than the isometric case in respect of both the rate at which collision outcomes can be determined, and in terms of the Reynolds coefficient. As a result of these improvements, the simulation time for the exact case mentioned above would reduce to the order of days, on the same hardware. This simulation time is sufficiently low for immediate practical application in the local environment

Inertial Coupling Method for particles in an incompressible fluctuating fluid

We develop an inertial coupling method for modeling the dynamics of point-like 'blob' particles immersed in an incompressible fluid, generalizing previous work for compressible fluids. The coupling consistently includes excess (positive or negative) inertia of the particles relative to the displaced fluid, and accounts for thermal fluctuations in the fluid momentum equation. The coupling between the fluid and the blob is based on a no-slip constraint equating the particle velocity with the local average of the fluid velocity, and conserves momentum and energy. We demonstrate that the formulation obeys a fluctuation-dissipation balance, owing to the non-dissipative nature of the no-slip coupling. We develop a spatio-temporal discretization that preserves, as best as possible, these properties of the continuum formulation. In the spatial discretization, the local averaging and spreading operations are accomplished using compact kernels commonly used in immersed boundary methods. We find that the special properties of these kernels make the discrete blob a particle with surprisingly physically-consistent volume, mass, and hydrodynamic properties. We develop a second-order semi-implicit temporal integrator that maintains discrete fluctuation-dissipation balance, and is not limited in stability by viscosity. Furthermore, the temporal scheme requires only constant-coefficient Poisson and Helmholtz linear solvers, enabling a very efficient and simple FFT-based implementation on GPUs. We numerically investigate the performance of the method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and associated discussion) relative to published versio

The iEBE-VISHNU code package for relativistic heavy-ion collisions

The iEBE-VISHNU code package performs event-by-event simulations for relativistic heavy-ion collisions using a hybrid approach based on (2+1)-dimensional viscous hydrodynamics coupled to a hadronic cascade model. We present the detailed model implementation, accompanied by some numerical code tests for the package. iEBE-VISHNU forms the core of a general theoretical framework for model-data comparisons through large scale Monte-Carlo simulations. A numerical interface between the hydrodynamically evolving medium and thermal photon radiation is also discussed. This interface is more generally designed for calculations of all kinds of rare probes that are coupled to the temperature and flow velocity evolution of the bulk medium, such as jet energy loss and heavy quark diffusion.Comment: 47 pages, 21 figures. Manuscript was accepted by Computer Physics Communication

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Numerical simulation of multifluid flows with the particle finite element method

In this monograph we have focused on understanding the basic physical principles of multi-fluid flows and the difficulties that arise in their numerical simulation. We have extended the Particle Finite Element Method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces. We have developed a numerical scheme able to deal with large jumps in the physical properties (density and viscosity), include surface tension, and accurately represent all types of discontinuities in the flow variables at the interface. The scheme is based on decoupling the nodes position, velocity and pressure variables through the Picard linearization and a pressure segregation method which takes into account the interface conditions. The interface has been defined to be aligned with the moving mesh, so that it remains sharp along time. Furthermore, pressure degrees of freedom have been duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity, and the mesh has been refined in the vicinity of the interface to improve the accuracy of the computations. We have applied the resulting scheme to several academic and geological problems,such as the two-fluid sloshing, extrusion of viscous fluids, bubble rise and breakup,mixing of magmatic liquids and negatively buoyant jets.Postprint (published version

Numerical simulation of multifluid flows with the particle finite element method

In this monograph we have focused on understanding the basic physical principles of multi-fluid flows and the difficulties that arise in their numerical simulation. We have extended the Particle Finite Element Method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces. We have developed a numerical scheme able to deal with large jumps in the physical properties (density and viscosity), include surface tension, and accurately represent all types of discontinuities in the flow variables at the interface. The scheme is based on decoupling the nodes position, velocity and pressure variables through the Picard linearization and a pressure segregation method which takes into account the interface conditions. The interface has been defined to be aligned with the moving mesh, so that it remains sharp along time. Furthermore, pressure degrees of freedom have been duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity, and the mesh has been refined in the vicinity of the interface to improve the accuracy of the computations

A generalised immersed boundary method for flows of dense suspension of solid particles

Immersed boundary method (IBM) provides computational advantages in approximating moving solid surfaces on fixed numerical meshes. It has been widely used for fully-resolved simulations of particulate flows. This thesis proposes a generalised formulation of IBM with improved applicability to flows with dense concentrations of particles and unstructured meshes. The new IBM formulation, which is based on the smooth-interface direct forcing approach, directly uses the algebraic discretised terms of the momentum equations in the evaluation of the forces on Lagrangian immersed boundary (IB) points, and evaluate the integral Lagrangian volumes based on these forces. Appropriate reconstructions of the boundary forces are adopted to ensure the compatibility with the momentum-weighted interpolation used for the finite-volume discretisation with a collocated mesh arrangement. A modified direct forcing formulation is also proposed, which results in an efficiency gain of a devised segregated flow-particle coupling scheme. The novel framework is applied to flows with stationary and moving IBs on both Cartesian and arbitrary triangular/tetrahedral meshes, and the results are similar or better than other related methods that are mostly developed for Cartesian meshes. Accurate and stable enforcement of the no-slip condition on the IB at every time-step is demonstrated, even for flows with strong transient behaviour and high velocity and pressure gradients. Local continuity in the vicinity of the IB is also preserved, ensuring local and global mass conservation alongside the local no-slip condition. Adaptations devised for unstructured meshes results in an accuracy close to that obtained on Cartesian meshes. The framework is successfully applied in the simulations of fluidisation of dense particle bed and a rising pack of light particles, showing robust stability. The issues related to the interfering regularised forces of different particle surfaces are not significant using the present formulation, hence eliminate unphysical flow patterns between aggregated particles.Open Acces