A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

Multilevel refinement for combinatorial optimisation problems

We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems.

Multilevel refinement for combinatorial optimisation: boosting metaheuristic performance

The multilevel paradigm as applied to combinatorial optimisation problems is a simple one, which at its most basic involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found, usually at the coarsest level, and then iteratively refined at each level, coarsest to finest, typically by using some kind of heuristic optimisation algorithm (either a problem-specific local search scheme or a metaheuristic). Solution extension (or projection) operators can transfer the solution from one level to another. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (for example multigrid techniques can be viewed as a prime example of the paradigm). Overview papers such as [] attest to its efficacy. However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial problems and in this chapter we discuss recent developments. In this chapter we survey the use of multilevel combinatorial techniques and consider their ability to boost the performance of (meta)heuristic optimisation algorithms.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

A multilevel study of area socio-economic status and food purchasing behaviour

Objective: This study examined the association between area socioeconomic status (SES) and food purchasing behaviour.----- Setting: Melbourne city, Australia, 2003.----- Participants: Residents of 2,564 households located in 50 small areas.----- Design: Data were collected by mail survey (64.2% response rate). Area SES was indicated by the proportion of households in each area earning less than Aus$400 per week, and individual-level socioeconomic position was measured using education, occupation, and household income. Food purchasing was measured on the basis of compliance with dietary guideline recommendations (for grocery foods) and variety of fruit and vegetable purchase. Multilevel regression examined the association between area SES and food purchase after adjustment for individual-level demographic (age, sex, household composition) and socioeconomic factors.----- Results: Residents of low SES areas were significantly less likely than their counterparts in advantaged areas to purchase grocery foods that were high in fibre and low in fat, salt, and sugar; and they purchased a smaller variety of fruits. There was no evidence of an association between area SES and vegetable variety.----- Conclusions In Melbourne, area SES was associated with some food purchasing behaviours independent of individual-level factors, suggesting that areas in this city may be differentiated on the basis of food availability, accessibility, and affordability, making the purchase of some types of foods more difficult in disadvantaged areas.

HABITAT : a longitudinal multilevel study of physical acitvity change in mid-aged adults

Purpose. To explore the role of the neighborhood environment in supporting walking Design. Cross sectional study of 10,286 residents of 200 neighborhoods. Participants were selected using a stratified two-stage cluster design. Data were collected by mail survey (68.5% response rate). Setting. The Brisbane City Local Government Area, Australia, 2007. Subjects. Brisbane residents aged 40 to 65 years. Measures. Environmental: street connectivity, residential density, hilliness, tree coverage, bikeways, and street lights within a one kilometer circular buffer from each resident’s home; and network distance to nearest river or coast, public transport, shop, and park. Walking: minutes in the previous week categorized as < 30 minutes, ≥ 30 < 90 minutes, ≥ 90 < 150 minutes, ≥ 150 < 300 minutes, and ≥ 300 minutes. Analysis. The association between each neighborhood characteristic and walking was examined using multilevel multinomial logistic regression and the model parameters were estimated using Markov chain Monte Carlo simulation. Results. After adjustment for individual factors, the likelihood of walking for more than 300 minutes (relative to <30 minutes) was highest in areas with the most connectivity (OR=1.93, 99% CI 1.32-2.80), the greatest residential density (OR=1.47, 99% CI 1.02-2.12), the least tree coverage (OR=1.69, 99% CI 1.13-2.51), the most bikeways (OR=1.60, 99% CI 1.16-2.21), and the most street lights (OR=1.50, 99% CI 1.07-2.11). The likelihood of walking for more than 300 minutes was also higher among those who lived closest to a river or the coast (OR=2.06, 99% CI 1.41-3.02). Conclusion. The likelihood of meeting (and exceeding) physical activity recommendations on the basis of walking was higher in neighborhoods with greater street connectivity and residential density, more street lights and bikeways, closer proximity to waterways, and less tree coverage. Interventions targeting these neighborhood characteristics may lead to improved environmental quality as well as lower rates of overweight and obesity and associated chromic disease.

Effects of switching time on output voltages of a multilevel inverter used in high frequency applications

Employing multilevel inverters is a proper solution to reduce harmonic content of output voltage and electromagnetic interference in high power electronic applications. In this paper, a new pulse width modulation method for multilevel inverters is proposed in which power devices’ on-off switching times have been considered. This method can be surveyed in order to analyse the effect of switching time on harmonic contents of output voltage in high frequency applications when a switching time is not negligible compared to a switching cycle. Fast Fourier transform calculation and analysis of output voltage waveforms and harmonic contents with regard to switching time variation are presented in this paper for a single phase (3, 5)-level inverters used in high voltage and high frequency converters. Mathematical analysis and MATLAB simulation results have been carried out to validate the proposed method.

Multilevel converters in renewable energy systems

In photovoltaic, fuel cells and storage batteries, the low output DC voltage should be boosted. Therefore, a step-up converter is necessary to boost the low DC voltage for the DC link voltage of the inverter. The main contribution of this chapter is to electrical energy conversion in renewable energy systems based on multilevel inverters. Different configuration of renewable energy systems based on power converters will be discussed in detail. Finally, a new single inductor Multi-Output Boost (MOB) converter is proposed, which is compatible with the diode-clamped configuration. Steady state and dynamic analyses have been carried out in order to show the validity of the proposed topology. Then the joint circuit of the proposed DC-DC converter with a three-level diode-clamped converter is presented in order to have a series regulated voltage at the DC link voltage of the diode-clamped inverter. MOB converter can boost the low input DC voltage of the renewable energy sources and at the same time adjust the voltage across each capacitor to the desired voltage levels, thereby solving the main problem associated with capacitor voltage imbalance in this type of multilevel converter.

A new predictive current control technique for multilevel converters

Multilevel inverters provide an attractive solution for power electronics when both reduced harmonic contents and high voltages are required. In this paper, a novel predictive current control technique is proposed for a three-phase multilevel inverter, which controls the capacitors voltages and load currents with low switching losses. The advantage of this contribution is that the technique can be applied to more voltage levels without significantly changing the control circuit. The three-phase three-level inverter with a pure inductive load has been implemented to track reference currents using analogue circuits and programmable logic device.