1,930 research outputs found
Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids
We use a modified Shan-Chen, noiseless lattice-BGK model for binary
immiscible, incompressible, athermal fluids in three dimensions to simulate the
coarsening of domains following a deep quench below the spinodal point from a
symmetric and homogeneous mixture into a two-phase configuration. We find the
average domain size growing with time as , where increases
in the range , consistent with a crossover between
diffusive and hydrodynamic viscous, , behaviour. We find
good collapse onto a single scaling function, yet the domain growth exponents
differ from others' works' for similar values of the unique characteristic
length and time that can be constructed out of the fluid's parameters. This
rebuts claims of universality for the dynamical scaling hypothesis. At early
times, we also find a crossover from to in the scaled structure
function, which disappears when the dynamical scaling reasonably improves at
later times. This excludes noise as the cause for a behaviour, as
proposed by others. We also observe exponential temporal growth of the
structure function during the initial stages of the dynamics and for
wavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review
Interface Tracking and Solid-Fluid Coupling Techniques with Coastal Engineering Applications
Multi-material physics arise in an innumerable amount of engineering problems. A broadly
scoped numerical model is developed and described in this thesis to simulate the dynamic interaction
of multi-fluid and solid systems. It is particularly aimed at modelling the interaction
of two immiscible fluids with solid structures in a coastal engineering context; however it can
be extended to other similar areas of research. The Navier Stokes equations governing the
fluids are solved using a combination of finite element (FEM) and control volume finite element
(CVFE) discretisations. The sharp interface between the fluids is obtained through the
compressive transport of material properties (e.g. material concentration). This behaviour is
achieved through the CVFE method and a conveniently limited flux calculation scheme based
on the Hyper-C method by Leonard (1991). Analytical and validation test cases are provided,
consisting of steady and unsteady flows. To further enhance the method, improve accuracy, and
exploit Lagrangian benefits, a novel moving mesh method is also introduced and tested. It is
essentially an Arbitrary Lagrangian Eulerian method in which the grid velocity is defined by
semi-explicitly solving an iterative functional minimisation problem.
A multi-phase approach is used to introduce solid structure modelling. In this approach,
solution of the velocity field for the fluid phase is obtained using Model B as explained by
Gidaspow (1994, page 151). Interaction between the fluid phase and the solids is achieved
through the means of a source term included in the fluid momentum equations. The interacting
force is calculated through integration of this source term and adding a buoyancy contribution.
The resulting force is passed to an external solid-dynamics model such as the Discrete Element
Method (DEM), or the combined Finite Discrete Element Method (FEMDEM).
The versatility and novelty of this combined modelling approach stems from its ability to
capture the fluid interaction with particles of random size and shape. Each of the three main
components of this thesis: the advection scheme, the moving mesh method, and the solid interaction
are individually validated, and examples of randomly shaped and sized particles are
shown. To conclude the work, the methods are combined together in the context of coastal engineering
applications, where the complex coupled problem of waves impacting on breakwater
amour units is chosen to demonstrate the simulation possibilities. The three components developed
in this thesis significantly extend the application range of already powerful tools, such
as Fluidity, for fluids-modelling and finite discrete element solids-modelling tools by bringing
them together for the first time
Frequency extraction for BEM-matrices arising from the 3D scalar Helmholtz equation
The discretisation of boundary integral equations for the scalar Helmholtz
equation leads to large dense linear systems. Efficient boundary element
methods (BEM), such as the fast multipole method (FMM) and H-matrix based
methods, focus on structured low-rank approximations of subblocks in these
systems. It is known that the ranks of these subblocks increase with the
wavenumber. We explore a data-sparse representation of BEM-matrices valid for a
range of frequencies, based on extracting the known phase of the Green's
function. Algebraically, this leads to a Hadamard product of a frequency matrix
with an H-matrix. We show that the frequency dependency of this H-matrix can be
determined using a small number of frequency samples, even for geometrically
complex three-dimensional scattering obstacles. We describe an efficient
construction of the representation by combining adaptive cross approximation
with adaptive rational approximation in the continuous frequency dimension. We
show that our data-sparse representation allows to efficiently sample the full
BEM-matrix at any given frequency, and as such it may be useful as part of an
efficient sweeping routine
Numerical methods for finding stationary gravitational solutions
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small rotating black holes in AdS. We also include several tools and tricks that have been useful throughout the literature
Non-iterative simulation methods for virtual analog modelling
The simulation of nonlinear components is central to virtual analog simulation. In audio effects, circuits often include devices such as diodes and transistors, mostly operating in a strongly nonlinear regime. Mathematical models are in the form of systems of nonlinear ordinary differential equations (ODEs), and traditional integrators, such as the trapezoid and midpoint methods, can be employed as solvers. These methods are fully implicit and require the solution of a nonlinear algebraic system at each time step, introducing further complications regarding the existence and uniqueness of the solution, as well as the choice of halting conditions for the iterative root finder. On the other hand, fast explicit methods such as Forward Euler, are prone to unstable behaviour at standard audio sample rates. For these reasons, in this work, a family of linearly-implicit schemes is presented. These schemes take the form of a perturbation expansion, making the construction of higher-order schemes possible. Compared with classic implicit designs, the proposed methods have the advantage of efficiency, since the update is computed in a single iteration. Furthermore, the existence and uniqueness of the update are proven by simple inspection of the update matrix. Compared to classic explicit designs, the proposed schemes display stable behaviour at standard audio sample rates. In the case of a single scalar ODE, sufficient conditions for numerical stability can be derived, imposing constraints on the choice of the sampling rate. Several theoretical results are provided, as well as numerical examples for typical stiff equations used in virtual analog modelling
Energy consistent nonlinear dynamic contact analysis of structures
This work is motivated by the need for a numerically stable dynamic contact algorithm, for use with finite element (FE) analysis including both material and geometric nonlinearities, which imposes the appropriate full kinematic compatibility between the interfaces of impacting boundaries during a persistent dynamic contact.
Several methods were previously developed based on Lagrangian multipliers or penalty functions in an attempt to impose the impenetrability condition of dynamic contact analysis. Some of these existing algorithms suffer from lack of numerical stability, and most of them are incapable of accurately predicting the persistent contact force, hence they would not be suitable for frictional dynamic contact analysis.
The numerical stability and energy conservation characteristics of conventional frictionless dynamic contact algorithms using Lagrangian displacement constraints and penalty functions are investigated in this thesis. Two energy controlling dynamic contact algorithms are proposed in conjunction with the well-known Newmark trapezoidal rule, namely, regularised penalty method and Lagrangian velocity constraint. Although energy consistent, the state of the art for these two methods is somewhat similar to the conventional displacement constraints in the sense that acceleration compatibility is not imposed when simulating problems featuring persistent dynamic contact.
In this work, a novel and superior energy controlling-algorithm is proposed which overcomes the aforementioned shortcomings. The proposed DVA method enforces the displacement, velocity and acceleration compatibilities (referred to as DVA constraint in this work) between the impacting interfaces, which in contrast to existing algorithms can be used for FE analysis of problems exhibiting geometric and material nonlinearities. The advanced DVA method is devised such that the kinematic compatibilities at the interface are consistent with the solution for a continuous system without any special treatment in the time-integration or solution procedure of the penetrating interface boundaries. Furthermore, this can be achieved in conjunction with all of the prevalent implicit time-integration schemes such as the trapezoidal rule, midpoint rule, HHT-α and the most recently developed Energy-Momentum family of Methods.
Finally, utilising the proposed dynamic contact algorithms, a novel multi-constraints node-to-surface dynamic contact element is formulated and programmed within a geometric and material nonlinear dynamic FE analysis software. Several verification examples of frictionless mechanical contact are presented to demonstrate the superiority and performance of the developed node-to-surface contact element in conjunction with the proposed DVA constraint as well as the Lagrangian velocity constraint, providing a robust and accurate solution procedure for highly nonlinear dynamic contact analysis.Open Acces
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