Hybrid finite difference/finite element immersed boundary method

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach employs a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach

Numerical investigation of the three-dimensional velocity fields induced by wave-structure interaction

Submerged shore-parallel breakwaters for coastal defence are a good compromise between the need to mitigate the effects of waves on the coast and the ambition to ensure the preservation of the landscape and water quality. In this work we simulate, in a fully three-dimensional form, the hydrodynamic effects induced by submerged breakwaters on incident wave trains with different wave height. The proposed three-dimensional non-hydrostatic finite-volume model is based on an integral form of the Navier-Stokes equations in σ-coordinates and is able to simulate the shocks in the numerical solution related to the wave breaking. The obtained numerical results show that the hydrodynamic phenomena produced by wave-structure interaction have features of three-dimensionality (undertow), that are locally important, and emphasize the need to use a non-hydrostatic fully-three-dimensional approach

Effective crustal permeability controls fault evolution: An integrated structural, mineralogical and isotopic study in granitic gneiss, Monte Rosa, Northern Italy

Two dextral faults within granitic gneiss in the Monte Rosa nappe, northern Italy reveal key differences in their evolution controlled by evolving permeability and water/rock reactions. The comparison reveals that identical host rock lithologies develop radically different mineralogies within the fault zones, resulting in fundamentally different deformation histories. Oxygen and hydrogen isotope analyses coupled to microstructural characterisation show that infiltration of meteoric water occurred into both fault zones. The smaller Virgin Fault shows evidence of periodic closed system behaviour, which promoted the growth of hydrothermal K-feldspar, whilst the more open system behaviour of the adjacent Ciao Ciao Fault generated a weaker muscovite-rich fault core, which promoted a step change in fault evolution. Effective crustal permeability is a vital control on fault evolution and, coupled to the temperature (i.e. depth) at which key mineral transformations occur, is probably a more significant factor than host rock strength in controlling fault development. The study suggests that whether a fault in granitic basement grows into a large structure may be largely controlled by the initial hydrological properties of the host rocks. Small faults exposed at the surface may therefore be evolutionary “dead-ends” that typically do not represent the early stages in the development of larger faults

Collective behavior of interacting self-propelled particles

We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the results of large scale simulations and theoretical approaches to the problem

Kinetic Solvers with Adaptive Mesh in Phase Space

An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for solving multi-dimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a tree of trees data structure. The mesh in r-space is automatically generated around embedded boundaries and dynamically adapted to local solution properties. The mesh in v-space is created on-the-fly for each cell in r-space. Mappings between neighboring v-space trees implemented for the advection operator in configuration space. We have developed new algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive mesh in velocity space: importance sampling, multi-point projection method, and the variance reduction method. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions in a Lorentz gas. New AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce computational cost and memory usage for solving challenging kinetic problems

The effect of small-amplitude time-dependent changes to the surface morphology of a sphere

Typical approaches to manipulation of flow separation employ passive means or active techniques such as blowing and suction or plasma acceleration. Here it is demonstrated that the flow can be significantly altered by making small changes to the shape of the surface. A proof of concept experiment is performed using a very simple time-dependent perturbation to the surface of a sphere: a roughness element of 1% of the sphere diameter is moved azimuthally around a sphere surface upstream of the uncontrolled laminar separation point, with a rotational frequency as large as the vortex shedding frequency. A key finding is that the non-dimensional time to observe a large effect on the lateral force due to the perturbation produced in the sphere boundary layers as the roughness moves along the surface is ˆt =tU_(∞)/D ≈4. This slow development allows the moving element to produce a tripped boundary layer over an extended region. It is shown that a lateral force can be produced that is as large as the drag. In addition, simultaneous particle image velocimetry and force measurements reveal that a pair of counter-rotating helical vortices are produced in the wake, which have a significant effect on the forces and greatly increase the Reynolds stresses in the wake. The relatively large perturbation to the flow-field produced by the small surface disturbance permits the construction of a phase-averaged, three-dimensional (two-velocity component) wake structure from measurements in the streamwise/radial plane. The vortical structure arising due to the roughness element has implications for flow over a sphere with a nominally smooth surface or distributed roughness. In addition, it is shown that oscillating the roughness element, or shaping its trajectory, can produce a mean lateral force

A ferrofluid based neural network: design of an analogue associative memory

We analyse an associative memory based on a ferrofluid, consisting of a system of magnetic nano-particles suspended in a carrier fluid of variable viscosity subject to patterns of magnetic fields from an array of input and output magnetic pads. The association relies on forming patterns in the ferrofluid during a trainingdphase, in which the magnetic dipoles are free to move and rotate to minimize the total energy of the system. Once equilibrated in energy for a given input-output magnetic field pattern-pair the particles are fully or partially immobilized by cooling the carrier liquid. Thus produced particle distributions control the memory states, which are read out magnetically using spin-valve sensors incorporated in the output pads. The actual memory consists of spin distributions that is dynamic in nature, realized only in response to the input patterns that the system has been trained for. Two training algorithms for storing multiple patterns are investigated. Using Monte Carlo simulations of the physical system we demonstrate that the device is capable of storing and recalling two sets of images, each with an accuracy approaching 100%.Comment: submitted to Neural Network