Sophisticated Numerical Techniques Research Articles

Novel modelling approach for evacuation strategies of tall towers - A case study of Lotus Tower

Rapid urbanisation and population growth have led to the construction of many high-rise and ultra-high-rise buildings globally. Concerns over evacuation of the occupants’ safety in extreme events such as fire or terrorist attacks are increasing. These issues have even restricted the height of tall buildings around the world. Major codes forbid the use of elevators in the event of a fire, unless they are specifically designed as evacuation elevators. However, elevators have known to be the most efficient way for vertical transport. In this work, a new approach of planning for overall emergency occupant egress through evacuation elevators is investigated using a sophisticated numerical modelling technique. The 350 m Lotus Tower, which is under construction in Colombo Sri Lanka, and going to be the tallest tower in South Asia, is taken as a case study to describe the evacuation methodology. The influence of important egress parameters such as the crowd flow density and evacuee demographics are also investigated. The work reported in this paper led to some layout changes in the Lotus Tower.

PD measurements, failure analysis, and control in high‐power IGBT modules

Increased voltage blocking capability and the development of packaging technology for IGBTs can enhance the local electric field that may become large enough to increase partial discharges (PDs) within the module. The study presents a survey on (i) simulation the electric field within an IGBT module; (ii) current standards for evaluation of the insulation systems of IGBTs; (iii) PD detection and localisation methods as well as other diagnostic and quality control test methods about IGBTs; and (iv) various methods for PD control in an IGBT module. The survey shows remarkable technical gaps in all four areas. More sophisticated numerical and theoretical techniques are needed to model complicated geometries, e.g. extremely sharp edges of the copper metallisation and protrusions in the substrate, and composite non-linear field grading materials. There is no model to take into account defects in the gel and on the ceramic substrate. IEC 61287-1 cannot sufficiently assess the behaviour of PDs on IGBT module under the actual operating conditions exposing fast rise pulse-width modulation-like voltages. There is no agreement on the exact origin and location of PDs in the module with relying on measured phase-resolved PD patterns. PD control methods using non-linear grading materials are not mature enough.

A Backprojection Slice Theorem for Tomographic Reconstruction.

Fast image reconstruction techniques are becoming important with the increasing number of scientific cases in high resolution micro and nano tomography. The processing of the large scale 3D data demands new mathematical tools for the tomographic reconstruction. Due to the high computational complexity of most current algorithms, big data sizes demands powerful hardware and more sophisticated numerical techniques. Several reconstruction algorithms are dependent on a mathematical tool called backprojection (a transposition process). A conventional implementation of the backprojection operator has cubic computational complexity. In the present manuscript we propose a new fast backprojection operator for the processing of tomographic data, providing a low-cost algorithm for this task. We compare our formula against other fast transposition techniques, using real and simulated large data sets.

Verification and validation of a rapid heat transfer calculation methodology for transient melt pool solidification conditions in powder bed metal additive manufacturing

A fundamental understanding of spatial and temporal thermal distributions is crucial for predicting solidification and solid-state microstructural development in parts made by additive manufacturing. While sophisticated numerical techniques that are based on finite element or finite volume methods are useful for gaining insight into these phenomena at the length scale of the melt pool (100–500μm), they are ill-suited for predicting engineering trends over full part cross-sections (>10×10cm) or many layers over long process times (>many days) due to the necessity of fully resolving the heat source characteristics. On the other hand, it is extremely difficult to resolve the highly dynamic nature of the process using purely in-situ characterization techniques [1]. This paper proposes a pragmatic alternative based on a semi-analytical approach to predicting the transient heat conduction during powder bed metal additive manufacturing processes. The model calculations were theoretically verified for selective laser melting of AlSi10Mg and electron beam melting of IN718 powders for simple cross-sectional geometries and the transient results are compared to steady state predictions from the Rosenthal equation. It is shown that the transient effects of the scan strategy create significant variations in the melt pool geometry and solid-liquid interface velocity, especially as the thermal diffusivity of the material decreases and the pre-heat of the process increases. With positive verification of the strategy, the model was then experimentally validated to simulate two point-melt scan strategies during electron beam melting of IN718, one intended to produce a columnar and one an equiaxed grain structure. Through comparison of the solidification conditions (i.e. transient and spatial variations of thermal gradient and liquid-solid interface velocity) predicted by the model to phenomenological CET theory, the model accurately predicted the experimental grain structures.

The science of complexity and the role of mathematics

In the middle of the second decade of the 21st century, Complexity Science has reached a turning point. Its rapid advancement over the last 30 years has led to remarkable new concepts, methods and techniques, whose applications to complex systems of the physical, biological and social sciences has produced a great number of exciting results. The approach has so far depended almost exclusively on the solution of a wide variety of mathematical models by sophisticated numerical techniques and extensive simulations that have inspired a new generation of researchers interested in complex systems. Still, the impact of Complexity beyond the natural sciences, its applications to Medicine, Technology, Economics, Society and Policy are only now beginning to be explored. Furthermore, its basic principles and methods have so far remained within the realm of high level research institutions, out of reach of society’s urgent need for practical applications. To address these issues, evaluate the current situation and bring Complexity Science closer to university students, a series of Ph.D. Schools on Mathematical Modeling of Complex Systems was launched, starting in July 2011 at the University of Patras, Greece (see http://www.math.upatras.gr/~phdsch11). These Schools lasted two weeks each and included, beyond introductory lectures, a conference component of 2–3 days where students were exposed to recent results mainly presented by young researchers. The Ph.D. Schools continued successfully, the 2nd one taking place at Pescara, Italy (2012), (see http://www.nodycosy.unich.it), the 3d one at Heraklion, Crete, Greece (2013) (see http://nlsconf2013.physics.uoc.gr) and the 4th one in Athens, Greece (2014) (see http://nlsconf2014.physics.uoc.gr) (2014). This Special Theme volume contains the proceedings of the 5th Ph.D. School-Conference of this series held at the University of Patras, Greece, 20 30 July, 2015 (see http://www.math.upatras.gr/~phdsch15) and includes many of the introductory lectures and research talks presented at this event. The primary concern of all those that participated in these events was to emphasize the role of mathematics, modeling and numerical simulation, which are indispensable for understanding what we call complex behavior of physical, biological, technological and socio – economical systems. In the discussions that took place, a great number of participants expressed the need to formulate a unifying theory of complex systems based on the main conclusions that have been reached so far in the science of Complexity. As Guest Editors of this volume, we also feel that it is important to reach some fundamental conclusions concerning common phenomena, theories and methodologies that arise in Complexity. We should all work to explore common rules and approaches, particularly in view of the remarkable challenges that face us all regarding complex social problems that threaten present day society and civilization as we know them.

Optimal experimental design for reservoir property estimates in geothermal exploration

During geothermal reservoir development, drilling deep boreholes turns out to be extremely expensive and risky. Thus, it is of great importance to work out the details of suitable borehole locations in advance. Here, given a set of existing boreholes, we demonstrate how a sophisticated numerical technique called optimal experimental design helps to find a location of an additional exploratory borehole that reduces risk and, ultimately, saves cost. More precisely, the approach minimizes the uncertainty when deducing the effective permeability of a buried reservoir layer from a temperature profile measured in this exploratory borehole. In this paper, we (1) outline the mathematical formulation in terms of an optimization problem, (2) describe the numerical implementation involving various software components, and (3) apply the method to a 3D numerical simulation model representing a real geothermal reservoir in northern Italy. Our results show that optimal experimental design is conceptually and computationally feasible for industrial-scale applications. For the particular reservoir and the estimation of permeability from temperature, the optimal location of the additional borehole coincides with regions of high flow rates and large deviations from the mean temperature of the reservoir layer in question. Finally, the presentation shows that, methodologically, the optimization method can be generalized from estimating permeability to finding any other reservoir properties.

The effect of high viscosity on the collapse-like chaotic and regular periodic oscillations of a harmonically excited gas bubble

In the last decade many industrial applications have emerged based on the rapidly developing ultrasonic technology such as ultrasonic pasteurization, alteration of the viscosity of food systems, and mixing immiscible liquids. The fundamental physical basis of these applications is the prevailing extreme conditions (high temperature, pressure and even shock waves) during the collapse of acoustically excited bubbles. By applying the sophisticated numerical techniques of modern bifurcation theory, the present study intends to reveal the regions in the excitation pressure amplitude–ambient temperature parameter plane where collapse-like motion of an acoustically driven gas bubble in highly viscous glycerine exists. We report evidence that below a threshold temperature the bubble model, the Keller–Miksis equation, becomes an overdamped oscillator suppressing collapse-like behaviour. In addition, we have found periodic windows interspersed with chaotic regions indicating the presence of transient chaos, which is important from application point of view if predictability is required.

Analytical Method of Temperature Prediction in Reinforced Concrete Beams

The determination of temperature profile within a reinforced concrete (RC) beam is essential for carrying out structural analysis at elevated temperatures. The temperatures are usually estimated using sophisticated numerical techniques which require computational support. Since the determination of rebar temperature in RC beams is more important than the concrete temperature a reliable analytical method of temperature prediction can become a helpful tool in simple beam analysis problems which are employed for determining residual strength in fire. This paper presents the details of development of an empirical equation for the prediction of temperature of rebar in RC beams. The equation is also capable of predicting concrete temperatures at different locations within the beam. The predictions made by the equation were compared with the temperatures determined from experimental beam testing and finite element (FE) analysis. A good correlation of the predicted temperatures was found for the entire time-temperature history with both the observed data and the estimated temperatures by FE models.

粗面開水路乱流の水面変動に及ぼす乱流渦構造の条件付き抽出に関する研究

In open-channel turbulence with relatively large Reynolds number, water surface is subject to various types of fluctuations depending on the strength of turbulence. The level of fluctuation varies also with the Froude number and several researches have been conducted with respect to the root-mean-square value of surface oscillation. However, the mechanism that creates such water surface features has not been executed in detail in terms of turbulence vortex structure especially in rough-wall turbulence. This research aims at extracting a vortex structure that directly affects the water surface phenomenon by using an experimental technique with PIV and a sophisticated numerical technique with LES. A three-dimensional vortex structure that has an impact on surface features was successfully extracted from the LES results by using a conditional sampling technique.

CFD Analysis of the Acoustic Behavior of a Centrifugal Compressor for High Performance Engine Application

The paper reports an activity aiming at the characterization of the acoustic noise of a centrifugal compressor for a currently made high performance engine. All the analyses are carried out through the use of Detached Eddy Simulation. During high-load/low- engine speed operations of the engine, the compressor exhibits noise peaks above 150 dBA at relatively low frequencies, whose origin is relatively hard to rationalize. The use of three-dimensional CFD simulation appears to be very promising to gain a better understanding of the complex flow structures at the compressor inlet as well as to promote design optimizations aiming at limiting the acoustic emissivity of the component. In view of the dependency of the acoustic phenomena on the instantaneous pressure waves and flow structures, fully transient CFD simulations are highly recommended, together with the use of sophisticated numerical techniques such as Large Eddy and Detached Eddy simulation [1], [2], which are widely recognized to be able to better capture highly unstable features than the common RANS approach [3], [4]. In order to limit the computational cost of the analyses, preliminary steady-state RANS simulations are carried out to both initialize the flow field and to evaluate the grid capability to properly match the desired frequency spectrum.

A novel model for biofilm growth and its resolution by using the hybrid immersed interface-level set method

In this work we propose a new model to simulate biofilm structures (“finger-like”, as well as, compact structures) as a result of microbial growth in different environmental conditions. At the same time, the numerical method that we use in order to carry out the computational simulations is new to the biological community, as far as we know. The use of our model sheds light on the biological process of biofilm formation since it simulates some central issues of biofilm growth: the pattern formation of heterogeneous structures, such as finger-like structures, in a substrate-transport-limited regime, and the formation of more compact structures, in a growth-limited-regime. The main advantage of our approach is that we consider several of the most relevant aspects of biofilm modeling, particularly, the existence and evolution of a biofilm–liquid interface. At the same time, in order to perform numerical simulations, we have used sophisticated numerical techniques based on mixing the immersed interface method and the level-set method, which are well described in the present work.

Problem of the Moving Boundary in Continuous Casting Solved by The Analytic-Numerical Method

Abstract Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase - liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

Simulations of Damage, Crack Initiation, and Propagation in Interlayer Dielectric Structures: Understanding Assembly-Induced Fracture in Dies

Performance enhancement by lowering the dielectric constant of interlayer dielectric (ILD) materials often compromises the mechanical integrity of the dielectric stack. At the present time, fracture in the ILD stacks induced by assembly to either an organic substrate or a die stack (3-D) is an important reliability consideration. These interactions include what is popularly referred to as the chip-package interactions. In this paper, we develop insights on the potential crack initiation site within the ILD, die-substrate geometrical parameters that cause most damage, as well as insights on the manufacturing process that is critical to failure. Towards this end, we utilize analytical models based on classical elasticity theory as well as sophisticated numerical techniques that are capable of nucleating and propagating cracks at arbitrary locations within the structure without remeshing. Specifically, we analytically estimate the strength of singularities at all the possible multimaterial corners in the ILD stack to provide insight on the likely damage nucleation sites for various material configurations in the ILD stack. Two novel numerical approaches are used for fracture simulation. In the first, cracks are modeled as discontinuous enrichments over an underlying continuous behavioral approximation. In the second approach, the underlying material description is enriched with a cohesive damage description whose stiffness is evolved according to a prescribed damage law. Multilevel finite-element models are used to determine the load imposed on the ILD structure by the substrate. Maximum damage induced in the ILD stack by the above load is used as an indicator of the reliability risk. Parametric simulations are conducted by varying ILD material, die size, die thickness, as well as the solder material. Through analytical models of bonded assemblies, we identify groups of relevant dimensionless parameters to relate the numerically estimated damage in ILD stacks to the die/substrate material and geometrical parameters. We demonstrate that the damage in the ILD stack is least when the flexural rigidity of the die is matched to that of the assembled substrate. We also demonstrate that ILD damage is only weakly correlated to shear deformation on the die surface due to assembly. We generalize the above observations into mathematical fits (for use as design rules) relating damage in ILD stacks to ILD material choice, relative substrate flexural rigidity, and die size.

Deformation Modulus of Fly Ash Modified with Lime and Gypsum

Deformation modulus of fly ash is one of the most important mechanical properties generally used in different design problems and also as an input parameter to sophisticated numerical techniques employed to assess the response of different structures resting on fly ash fill or embankment made of fly ash. Deformation modulus is usually expressed in terms of compressive strength. This paper presents the deformation modulus of fly ash modified with lime alone or in combination with gypsum at different strain levels. The values of deformation modulus obtained from both unconfined compression test and unconsolidated undrained triaxial test results are presented herein. The specimens for unconfined compression test and for undrained triaxial tests were cured up to 90 and 28 days, respectively. The effects of addition of lime (4–10%) and gypsum (0.5 and 1.0%) on the deformation modulus of class F fly ash are highlighted. With addition of lime and gypsum, the class F fly ash achieved the deformation modulus in the range of 190 MPa in UCS test and up to 300 MPa in triaxial test specimens tested under all round pressure of 0.4 MPa. Based on the present test results empirical relationships are developed to estimate deformation modulus of modified fly ash from unconfined compressive strength and relationships between initial tangent modulus and secant modulus at different strain levels are also developed.

Assessment of structural sensitivity on the basis of artificial neural networks

AbstractIn engineering practice, the assessment of sensitivity is utilized to detect influential parameters in order to facilitate subsequent numerical simulation techniques. As sensitivity analyses are preprocessing methods for sophisticated numerical simulation techniques, e.g. reliability based optimization procedures, their application is always linked to an increase of the computational expense. In result, it is reasonable to couple sensitivity analysis and artificial neural networks (ANN). Therefore, multi‐faceted global sensitivity measures (GSM) may be formulated, taking advantage of different characteristics of the ANNs. Additionally, to take into account nonlinearities of the response surface, a new approach of sectional global n sensitivity measures is introduced. Generally, the sensitivity can be determined with $S_{i}=\hat{S}_{i}/\sum\limits_{j=1}^{n}\hat{S}_{j}$. Thereby, $S_{i}$ denotes the sensitivity of interest and $\hat{S}_{i}$ a characteristic of the function $f:\mathcal{R}^n\rightarrow\mathcal{R}$ under investigation. This can be either the response $f$ itself or the first partial derivative thereof $\partial_{i}f$. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Including lateral velocity variations into true-amplitude common-shot wave-equation migration

In heterogeneous media, standard one-way wave equations describe only the kinematic part of one-way wave propagation correctly. For a correct description of amplitudes, the one-way wave equations must be modified. In media with vertical velocity variations only, the resulting true-amplitude one-way wave equations can be solved analytically. In media with lateral velocity variations, these equations are much harder to solve and require sophisticated numerical techniques. We present an approach to circumvent these problems by implementing approximate solutions based on the one-dimensional analytic amplitude modifications. We use these approximations to show how to modify conventional migration methods such as split-step and Fourier finite-difference migrations in such a way that they more accurately handle migration amplitudes. Simple synthetic data examples in media with a constant vertical gradient demonstrate that the correction achieves the recovery of true migration amplitudes. Applications to the SEG/EAGE salt model and the Marmousi data show that the technique improves amplitude recovery in the migrated images in more realistic situations.

Large Dynamic Range Simulations of Galaxies Hosting Supermassive Black Holes

AbstractThe co-evolution of supermassive black holes (SMBHs) and their host galaxies is a rich problem, spanning a large-dynamic range and depending on many physical processes. Simulating the transport of gas and angular momentum from super-galactic scales all the way down to the outer edge of the black hole's accretion disk requires sophisticated numerical techniques with extensive treatment of baryonic physics. We use a hydrodynamic adaptive mesh refinement simulation to follow the growth and evolution of a typical disk galaxy hosting an SMBH, in a cosmological context (covering a dynamical range of 10 million!). We have adopted a piecemeal approach, focusing our attention on the gas dynamics in the central few hundred parsecs of the simulated galaxy (with boundary conditions provided by the larger cosmological simulation), and beginning with a simplified picture (no mergers or feedback). In this scenario, we find that the circumnuclear disk remains marginally stable against catastrophic fragmentation, allowing stochastic fueling of gas into the vicinity of the SMBH. I will discuss the successes and the limitations of these simulations, and their future direction.

On the use of advanced numerical models for the evaluation of dosimetric parameters and the verification of exposure limits at workplaces

With the next transposition of the 2004/40/EC Directive, employers will become responsible for the electromagnetic field level at the workplace. To make this task easier, the scientific community is compiling practical guidelines to be followed. This work aims at enriching such guidelines, especially for the dosimetric issues. More specifically, some critical aspects related to the application of numerical dosimetric techniques for the verification of the safety limit compliance have been highlighted. In particular, three different aspects have been considered: the dosimetric parameter dependence on the shape and the inner characterisation of the exposed subject as well as on the numerical algorithm used, and the correlation between reference limits and basic restriction. Results and discussions demonstrate how, even by using sophisticated numerical techniques, in some cases a complex interpretation of the result is mandatory.

The growth factor of a Hadamard matrix of order 16 is 16

AbstractIn 1968 Cryer conjectured that the growth factor of an n × n Hadamard matrix is n. In 1988 Day and Peterson proved this only for the Hadamard–Sylvester class. In 1995 Edelman and Mascarenhas proved that the growth factor of a Hadamard matrix of order 12 is 12. In the present paper we demonstrate the pivot structures of a Hadamard matrix of order 16 and prove for the first time that its growth factor is 16. The study is divided in two parts: we calculate pivots from the beginning and pivots from the end of the pivot pattern. For the first part we develop counting techniques based on symbolic manipulation for specifying the existence or non‐existence of specific submatrices inside the first rows of a Hadamard matrix, and so we can calculate values of principal minors. For the second part we exploit sophisticated numerical techniques that facilitate the computations of all possible (n − j) × (n − j) minors of Hadamard matrices for various values of j. The pivot patterns are obtained by utilizing appropriately the fact that the pivots appearing after the application of Gaussian elimination on a completely pivoted matrix are given as quotients of principal minors of the matrix. Copyright © 2009 John Wiley & Sons, Ltd.

Comment on “Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets”

Quantum Monte Carlo methods are sophisticated numerical techniques for simulating interacting quantum systems. In some cases, however, they suffer from the notorious ``sign problem'' and become too inefficient to be useful. A recent publication [J. Wojtkiewicz, Phys. Rev. B 75, 174421 (2007)] claims to have solved the sign problem for a certain class of frustrated quantum spin systems through the use of a bipartite valence bond basis. We show in this Comment that the apparent positivity of the path integral is due to a misconception about the resolution of the identity operator in this basis and that consequently the sign problem remains a severe obstacle for the simulation of frustrated quantum magnets.