Free-surface modelling (FSM) is a highly relevant and computationally intensive area of study in modern computational fluid dynamics. The Elemental software suite currently under development offers FSMcapability, and employs a preconditioned GMRES solver in an attempt to effect fast solution times. In terms of potential solver performance however, multigrid methods can be considered state-of-the-art. This work details the investigation into the use of AlgebraicMultigrid (AMG) as a high performance solver tool for use as black box plug-in for Elemental FSM. Special attention was given to the development of novel and robust methods of addressing AMG setup costs in addition to transcribing the solver to efficient C++ object-oriented code. This led to the development of the so-called Freeze extension of the basic algebraic multigrid method in an object-oriented C++ programming environment. The newly developed Freeze method reduces setup costs by periodically performing the setup procedure in an automatic and robust manner. The developed technology was evaluated in terms of robustness, stability and speed by applying it to benchmark FSM problems on structured and unstructured meshes of various sizes. This evaluation yielded a number of conclusive findings. First, the developed Freeze method reduced setup times by an order of magnitude. Second, the developed AMG solver offered substantial performance increases over the preconditioned GMRES method. In this way, it is proposed that this work has furthered the state-of-the-art of algebraic multigrid methods applied in the context of free-surface modelling. / Dissertation (MEng)--University of Pretoria, 2011. / Mechanical and Aeronautical Engineering / unrestricted

Please read the abstract in the dissertation. / Dissertation (MEng)--University of Pretoria, 2013. / gm2014 / Civil Engineering / Unrestricted

One of the most interesting extraterrestrial bodies in the Solar System is Europa, the icy satellite of Jupiter. This icy moon might have a sufficiently hospitable environment which could be harbouring life in the subsurface ocean deep under its icy crust. The thesis thoroughly examines the generation process of one of the surface formations called chaotic terrains. These huge areas of ice disruptions which uniquely characterize Europa's surface might play a significant role in the understanding of the inner structure of the moon. The latest research assumes the chaotic terrains form above liquid water lenses perched relatively shallow in the ice shell, however, no numerical simulations have been performed to confirm this theory. The goal of the thesis is to create a model which would validate the theory and explain the formation process of the chaotic terrains. The thesis runs several simulations, and our results suggest these water lenses and the process in the mantle might play a key role in the chaotic terrains formation.

Parametric resonance is a particular type of resonance in which a parameter in a system changes with time. A particularly interesting case is when the parameter changes in a periodic way, which can lead to very intricate behavior. This di↵ers from periodic forcing in that solutions are not necessarily periodic. A system in which parametric resonance is realized is when a fluid bath is shaken periodically, which leads to an e↵ective time dependent gravitational force. This system will be used to study the onset of surface waves in a bath with non-uniform topography. A linear model for the surface waves is derived from the Euler equations in the limit of shallow waves, which includes the geometry of the bottom and surface tension. Experiments are performed to compare with the proposed model and good qualitative agreement is found. Another experiment which relies on a shaking fluid bath is that of bouncing fluid droplets. In the case of two droplets the shaking allows for a larger bouncing droplet to attract a smaller moving droplet in a way that creates a bound system. This bound system is studied and shows some analogous properties to quantum systems, so a quantum mechanical model for a two dimensional atom is studied, as well as a proposed model for the droplet-wave system in terms of equations of fluid mechanics.

In this paper the popup height of rising buoyant spheres is studied over a range of distinct release depths along with the accompanying velocities and accelerations near the free surface. In the past, regimes of motion due to vortex induced vibrations have been classified based on trajectories below the free surface. This study focuses on the popup height, velocity and acceleration at free surface exit, and vortex shedding in order to further define regimes of motion experienced by a rising buoyant sphere. Varying the release depth below the free surface reveals varying exit angles, velocities, accelerations, and popup heights at surface exit. Vortex shedding prior to free surface exit causes decelerations contributing to the variation in exit velocities and resulting popup heights. Using high-speed imaging and particle image velocimetry, we examine the trajectories, accelerations, velocities and vortex shedding events for spheres of different mass ratios over a range of Reynolds number (2e4 >Re> 6e5). At lower Re, spheres released from shallow release depths result in greater accelerations and velocities at free surface exit along with greater popup heights compared to releases from deeper depths. After reaching a depth which results in a minimum popup height, further increasing the release depth reveals an increase in popup height demonstrating an oscillatory pattern due to the sphere being released from vortex forces after shedding. This pattern is repeated as the popup height again decreases with greater release depths. For spheres of greater Re, popup height increases linearly with release depth, demonstrating continued accelerations at free surface exit.

Of the surface capturing schemes, the levelset and multi-phase models are implemented and extensively examined. First, the levelset method is shown, and its weaknesses are identified; a mis- appropriation of changes in momentum, a strong dependence on the density by the eigenvalues of the inviscid flux Jacobian, and a prescribed density transition. These weaknesses are specifically addressed and overcome by the formulation of the multi-phase model. Consequently, the multi-phase model is chosen for this work. Previous surface fitting techniques simply absorb the gravitational source term into the pressure. It must be noted that this absorbtion is valid only for single density flows; since the surface fitting approach is solving only one side of the interface, there is no significant change in the density througout the domain. Consequently, absorbing the gravitational source into the pressure term is not possible in a surface capturing scheme in which both sides of the interface are solved. Thus, a new treatment of the gravitational source term is required and is presented in this work. A multi-phase model is implemented into a parallel, three-dimensional, unsteady, incompressible Navier-Stokes flow solver for the purpose of examining free surface flows on unstructured meshes. The reasons for choosing this model above others are presented, and the multi-phase model is discussed. The base algorithm is briefly examined with emphasis given to the areas which require additional care. The construction of the gravity source term which drives the formation of the waves is explained in detail, and its effects on the rest of the algorithm are identified. Finally, the method is carefully compared with available data on a submerged NACA 0012 airfoil, the Wigley Hull, the Series 60 Cb=0.6 ship, and the DTMB 5415 ship.

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No / An incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces. The basic equations solved are the incompressible mass conservation and Navier¿Stokes equations. The method uses prediction¿correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting deviation of particle density is then implicitly projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. Various SPH formulations are employed in the discretization of the relevant gradient, divergence and Laplacian terms. Free surfaces are identified by the particles whose density is below a set point. Wall boundaries are represented by particles whose positions are fixed. The SPH formulation is also extended to non-Newtonian flows and demonstrated using the Cross rheological model. The incompressible SPH method is tested by typical 2-D dam-break problems in which both water and fluid mud are considered. The computations are in good agreement with available experimental data. The different flow features between Newtonian and non-Newtonian flows after the dam-break are discussed.