Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)

A front-tracking method for the computations of multiphase flow

The numerical simulation of flows with interfaces and free-surface flows is a vast topic, with applications to domains as varied as environment, geophysics, engineering, and fundamental physics. In engineering, as well as in other disciplines, the study of liquid-gas interfaces is important in combustion problems with liquid and gas reagents. The formation of droplet clouds or sprays that subsequently burn in combustion chambers originates in interfacial instabilities, such as the Kelvin-Helmholtz instability. What can numerical simulations do to improve our understanding of these phenomena? The limitations of numerical techniques make it impossible to consider more than a few droplets or bubbles. They also force us to stay at low Reynolds or Weber numbers, which prevent us from finding a direct solution to the breakup problem. However, these methods are potentially important. First, the continuous improvement of computational power (or, what amounts to the same, the drop in megaflop price) continuously extends the range of affordable problems. Second, and more importantly, the phenomena we consider often happen on scales of space and time where experimental visualization is difficult or impossible. In such cases, numerical simulation may be a useful prod to the intuition of the physicist, the engineer, or the mathematician. A typical example of interfacial flow is the collision between two liquid droplets. Finding the flow involves the study not only of hydrodynamic fields in the air and water phases but also of the air-water interface. This latter part

Direct numerical simulation of free-surface and interfacial flow

Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of the 19th century. Linear stability theory governs the onset of breakup and was developed by Rayleigh, Plateau, and Maxwell. However, only recently has attention turned to the nonlinear behavior in the vicinity of the singular point where a drop separates. The increased attention is due to a number of recent and increasingly refined experiments, as well as to a host of technological applications, ranging from printing to mixing and fiber spinning. The description of drop separation becomes possible because jet motion turns out to be effectively governed by one-dimensional equations, which still contain most of the richness of the original dynamics. In addition, an attraction for physicists lies in the fact that the separation singularity is governed by universal scaling laws, which constitute an asymptotic solution of the Navier-Stokes equation before and after breakup. The Navier-Stokes equation is thus continued uniquely through the singularity. At high viscosities, a series of noise-driven instabilities has been observed, which are a nested superposition of singularities of the same universal form. At low viscosities, there is rich scaling behavior in addition to aesthetically pleasing breakup patterns driven by capillary waves. The author reviews the theoretical development of this field alongside recent experimental work, and outlines unsolved problems.

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Nonlinear dynamics and breakup of free-surface flows

Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects

Physics of liquid jets

Modelling Merging and Fragmentation in Multiphase Flows with SURFER

Several studies have shown the existence of significant differences in the rate of new business creation between men and women. Specifically, it has been shown that women are much less likely to be involved in entrepreneurship than men worldwide. It is not yet understood, however, if such differences are the result of personal characteristics of the individual and of her economic environment or are, instead, the result of universal and, perhaps, evolutionary phenomena. Our empirical analysis is conducted using representative samples of population for 37 countries and a special form of bootstrapping that allows us to equalize individuals’ conditions and, as a result, analyze the choices of men and women put in identical economic environments and socio-economic circumstances.

Being in Someone Else’s Shoes: the Role of Gender in Nascent Entrepreneurship

The spatial structure and temporal evolution of coherent MHD modes in fusion plasma devices have been so far inferred from the experimental signals by using spectral techniques. Considering the data as a collection of n-dimensional discrete time series xi(t) permits one to introduce in this context a signal processing method based on the singular value decomposition (SVD) of a rectangular matrix. This paper shows that, whereas the SVD is equivalent to the discrete Fourier transform in the case of travelling sinusoidal waves, in more realistic cases it is a clear improvement on the spectral methods, since it disentangles the poloidal structure without a priori knowledge. Various applications of SVD, first on artificial signals and then on magnetic and SXR signals detected in the JET Tokamak in several plasma regimes, are shown with the purpose of illustrating the power and limits of the method.

https://iopscience.iop.org/article/10.1088/0741-3335/34/9/001/pdf

Multichannel fluctuation data analysis by the singular value decomposition method. Application to MHD modes in JET

Echo-reconstruction techniques for non-intrusive imaging have wide application, from subsurface and underwater imaging to medical and industrial diagnostics. The techniques are based on experiments in which a collection of short acoustic or electromagnetic impulses, emitted at the surface, illuminate a certain volume and are backscattered by inhomogeneities of the medium. The inhomogeneities act as re ecting surfaces or interfaces which cause signal echoing; the echoes are then recorded at the surface and processed through a \"computational lens\" de ned by a propagation model to yield an image of the same inhomogeneities. The most sophisticated of these processing techniques involve simple acoustic imaging in seismic exploration, for which the huge data sets and stringent performance requirements make high performance computing essential.

/pdf/phase-shift-plus-interpolation-a-scheme-for-high-performance-4g6z0kjqve.pdf

Phase shift plus interpolation: a scheme for high-performance echo-reconstructive imaging

Comparative studies of methods of reverse time migration (RTM) show that spectral methods for calculating the Laplacian impose the least stringent demands on discretization stepsize; thus with spectral methods, the grid re nements often required by other methods can be avoided. Implemented with absorbing boundary conditions, which are energy-tuned to give good absorption at the boundaries, these spectral methods can be used e ectively for migration, without su ering the problems of wraparound which have traditionally plagued them (Furumyra and Takenaka, 1995).

/pdf/3d-spectral-reverse-time-migration-with-no-wraparound-4x33tqic81.pdf

Carlo Nardone

Papers

Modelling Merging and Fragmentation in Multiphase Flows with SURFER

Being in Someone Else’s Shoes: the Role of Gender in Nascent Entrepreneurship

Multichannel fluctuation data analysis by the singular value decomposition method. Application to MHD modes in JET

Phase shift plus interpolation: a scheme for high-performance echo-reconstructive imaging

3D spectral reverse time migration with no‐wraparound absorbing conditions