Multiscale Concept Research Articles

Fundamental Numerical Simulation of Microbubble Interaction Using Multi-scale Multiphase Flow Equation

Modeling gas–liquid interfaces is a key issue in numerical research on multiphase flows. In particular, the mechanism of bubble coalescence/repulsion has not yet been clarified, and thus far, no valid numerical models have been developed. The mechanism may be related to thermodynamics, electromagnetics, hydrodynamics, and heat and mass transfer. Experimental studies have revealed that the concentration of electrolyte dissolved in water and the ion pairs affect bubble coalescence. Contamination such as ions adsorbed at the interface cannot be ignored when considering interfacial interaction. Interfacial effects may be more significant than gravitational effects especially when considering microbubble interactions. Therefore, it is necessary to consider such interfacial effects on microbubble coalescence when developing a gas–liquid interfacial model. In our previous study, we assumed that the interface exists as a thin fluid membrane with finite thickness. Then, we developed a new gas–liquid interfacial model on the basis of thermodynamic and mathematical approaches. In that study, a new governing equation was derived by incorporating the free energy, including the electrostatic potential due to contamination at the interface, into the conventional Navier–Stokes equation on the basis of a multi-scale concept. In the present study, a numerical test was performed for evaluating the surface tension effect of our new interfacial model. Then, the new governing equation was qualitatively evaluated by simulating the interaction between two microbubbles. In the simulation, we investigated microbubble behavior by considering electrostatic potentials of different magnitudes.

Strategy for predicting effective transport properties of complex porous structures

Measurements of effective transport properties of porous media, such as effective diffusivity and permeability, are well established by several experimental techniques. Effective transport properties can be also calculated from the spatially 3D reconstructed porous media, where the morphology characteristics required for the reconstruction are obtained from electron microscopy images. Here we demonstrate the reconstruction of porous alumina catalyst carrier with bimodal pore size distribution. Multi-scale concept is employed for the computation of effective diffusivity and permeability of reconstructed porous media and calculated effective transport properties are compared with transport parameters experimentally determined in Graham diffusion and simple permeation cell. The limitations of current state-of-the-art reconstruction techniques for porous media with broad pore size distribution are discussed. We show that the contribution of nano-pores towards the total diffusion flux is significant and cannot be neglected, but it is reasonable to neglect the contribution of nano-pores towards the sample permeability.

Modeling finite deformations in trigonal ceramic crystals with lattice defects

A model is developed for thermomechanical behavior of defective, low-symmetry ceramic crystals such as α -corundum. Kinematics resolved are nonlinear elastic deformation, thermal expansion, dislocation glide, mechanical twinning, and residual lattice strains associated with eigenstress fields of defects such as dislocations and stacking faults. Multiscale concepts are applied to describe effects of twinning on effective thermoelastic properties. Glide and twinning are thermodynamically irreversible, while free energy accumulates with geometrically necessary dislocations associated with strain and rotation gradients, statistically stored dislocations, and twin boundaries. The model is applied to describe single crystals of corundum. Hardening behaviors of glide and twin systems from the total density of dislocations accumulated during basal slip are quantified for pure and doped corundum crystals. Residual lattice expansion is predicted from nonlinear elasticity and dislocation line and stacking fault energies.

Development of Local Heat Transfer Models for Safety Assessment of High Temperature Gas-Cooled Reactor Cores—Part I: Pebble Bed Reactors

This and the subsequent paper present models developed for determining fuel particle and fuel element temperatures in normal operation and transient conditions in high temperature reactor cores. Multiscale modeling concepts are used to develop the models for both pebble bed and prismatic core types. This paper, Part I, presents the development of the model for pebble bed reactors. Comparison is made with finite element simulations of an idealized “two-dimensional” pebble in transient conditions, and with a steady-state analytical solution in a spherical pebble geometry. A method is presented for determining the fuel temperatures in the individual batches of a multibatch recycle refuelling regime. Implementation of the multiscale and multibatch fuel models in a whole-core computational fluid dynamics model is discussed together with the future intentions of the research program.

Multi-scale digital terrain analysis and feature selection for digital soil mapping

Terrain attributes are the most widely used predictors in digital soil mapping. Nevertheless, discussion of techniques for addressing scale issues and feature selection has been limited. Therefore, we provide a framework for incorporating multi-scale concepts into digital soil mapping and for evaluating these scale effects. Furthermore, soil formation and soil-forming factors vary and respond at different scales. The spatial data mining approach presented here helps to identify both the scale which is important for mapping soil classes and the predictive power of different terrain attributes at different scales. The multi-scale digital terrain analysis approach is based on multiple local average filters with filter sizes ranging from 3 × 3 up to 31 × 31 pixels. We used a 20-m DEM and a 1:50 000 soil map for this study. The feature space is extended to include the terrain conditions measured at different scales, which results in highly correlated features (terrain attributes). Techniques to condense the feature space are therefore used in order to extract the relevant soil forming features and scales. The prediction results, which are based on a robust classification tree (CRUISE) show that the spatial pattern of particular soil classes varies at characteristic scales in response to particular terrain attributes. It is shown that some soil classes are more prevalent at one scale than at other scales and more related to some terrain attributes than to others. Furthermore, the most computationally efficient ANOVA-based feature selection approach is competitive in terms of prediction accuracy and the interpretation of the condensed datasets. Finally, we conclude that multi-scale as well as feature selection approaches deserve more research so that digital soil mapping techniques are applied in a proper spatial context and better prediction accuracy can be achieved.

Application of the multiscale FEM to the modeling of cancellous bone

This paper considers the application of multiscale finite element method (FEM) to the modeling of cancellous bone as an alternative for Biot's model, the main intention of which is to decrease the extent of the necessary laboratory tests. At the beginning, the paper gives a brief explanation of the multiscale concept and thereafter focuses on the modeling of the representative volume element and on the calculation of the effective material parameters, including an analysis of their change with respect to increasing porosity. The latter part of the paper concentrates on the macroscopic calculations, which is illustrated by the simulation of ultrasonic testing and a study of the attenuation dependency on material parameters and excitation frequency. The results endorse conclusions drawn from the experiments: increasing excitation frequency and material density cause increasing attenuation.

Multiscale molecular modeling in nanostructured material design and process system engineering

Atomistic-based simulations such as molecular mechanics, molecular dynamics, and Monte Carlo-based methods have come into wide use for material design. Using these atomistic simulation tools, we can analyze molecular structure on the scale of 0.1–10 nm. However, difficulty arises concerning limitations of the time and length scale involved in the simulation. Although a possible molecular structure can be simulated by the atom-based simulations, it is less realistic to predict the mesoscopic structure defined on the scale of 100–1000 nm, for example the morphology of polymer blends and composites, which often dominates actual material properties. For the morphology on these scales, mesoscopic simulations such as the dynamic mean field density functional theory and dissipative particle dynamics are available as alternatives to atomistic simulations. It is therefore inevitable to adopt a mesoscopic simulation technique and bridge the gap between atomistic and mesoscopic simulations for an effective material design. Furthermore, it is possible to transfer the simulated mesoscopic structure to finite elements modeling tools for calculating macroscopic properties for the systems of interest. In this contribution, a hierarchical procedure for bridging the gap between atomistic and macroscopic modeling passing through mesoscopic simulations will be presented and discussed. The concept of multiscale (or many scale) modeling will be outlined, and examples of applications of single scale and multiscale procedures for nanostructured systems of industrial interest will be presented. In particular the following industrial applications will be considered: (i) polymer-organoclay nanocomposites of a montmorillonite–polymer–surface modifier system; (ii) mesoscale simulation for diblock copolymers with dispersion of nanoparticels; (iii) polymer–carbon nanotubes system and (iv) applications of multiscale modeling for process systems engineering.

Multiscale Design and Modeling of Protein-based Nanomechanisms for Nanorobotics

In this paper, we present a novel approach that makes use of multiscale and multiphysics modeling coupled to virtual reality for nanorobotic prototyping systems. First, a CAD-assisted assembly system that integrates principles for a multiscale approach into a nanorobotics structure design is presented. Then, we focus on the different design levels, more specifically, the optimization of geometry structure carried out by quantum mechanics, molecular dynamics and continuum mechanics methodologies. As an illustration of the proposed multiscale modeling concepts, we test the dynamic characteristics of a molecular sarcomere mechanism through steered molecular dynamics (SMD) simulations. The nano-kinematic parallel platform is composed of protein-based passive kinematic chains and actuated by myosin actuators. Multiscale simulations and experiments prove the effectiveness and accuracy of the proposed design and modeling approaches.

A Reflectarray Antenna Based on Multiscale Phase-Shifting Cell Concept

A novel phase shifting cell design is presented for microstrip reflectarrays. It uses a multiscale concept that consists of adaptively modifying the cell size over the reflectarray. A 1563deg phase range is demonstrated. A Ku-band reflectarray is manufactured and measured.

Use of CAPE-OPEN standards in the interoperability between modelling tools (MoT) and process simulators (Simulis ® Thermodynamics and ProSimPlus)

Computer-aided design, analysis and/or operation of chemical products and processes that manufacture them require a number of computational tools. As these tools may come from different sources and disciplines, an important issue is how they can be used simultaneously and efficiently for the design, analysis and/or simulation of a specific process-product? One alternative is to employ CAPE-OPEN standard interfaces for integration of the set of diverse computational tools that may be needed to solve the problem. The objective of this paper is to highlight, through examples, the integration of different computational tools according to problem specific work-flows/data-flows. The reliability of the integration of different tools is illustrated through two case studies. In case study 1, the tools Simulis ® Thermodynamics (PME) and ICAS-MoT (PMC) are combined for the calculation of thermodynamic properties through the use of a standard middleware (DLL file). In case study 2, the interoperability between ProSimPlus simulator (PME) and ICAS-MoT (PMC) is highlighted for simulation of a new unit operation and combined with other unit operations that can be found in the host simulator. A ProSimPlus-ICAS-MoT–COFE interoperability is also carried out successfully to proof the interoperability of the different computational entities. Furthermore, the introduction of the multiscale modelling concept and its application through the CAPE-OPEN standards is highlighted.

Non-local stress gradient approach for multiaxial fatigue of defective material

The fatigue crack initiation from a surface defect is analysed by means of a new attempt based on multiscale reduction of the stress distribution along the potential crack initiation plane. The reduction is performed by averaging process for shear and normal stresses over two critical areas (multiscale concept). The Matake multiaxial fatigue failure criterion was used to combine the effect of the reduced shear and normal stresses and to calculate the equivalent fatigue strength. The results were verified on defective material subjected to proportional loading. Elastic–plastic numerical simulations were performed for each defect geometry and type of loading (tension, torsion, and tension–torsion) to determine stress distribution. The analysis reveals that the proper calculation of the fatigue limit for defective materials requires performing the averaging process for shear and normal stresses separately.

Multi-scale modeling of three-phase–three-component processes in heterogeneous porous media

Flow and transport processes in porous media occur on different spatial and temporal scales and may also be locally different. Additionally, the structure of the porous medium itself generally shows a high dependence on the spatial scale. As an example, the contamination of the unsaturated zone with a light non-aqueous phase liquid is studied, corresponding to a domain with randomly distributed heterogeneities where complex three-phase–three-component processes are relevant only in a small (local) subdomain. This subdomain needs fine resolution as the complex processes are governed by small-scale effects. For a comprehensive fine-scale model taking into account three-phase–three-component processes as well as heterogeneities in the whole (global) model domain, data collection is expensive and computational time is long. Therefore, we developed a general multi-scale concept where on the one hand, the global flow field influences the local three-phase–three-component processes on the fine-scale. On the other hand, a coarse-scale saturation equation is solved where the effects of the fine-scale multi-phase–multi-component processes in the subdomain are captured by source/sink terms and the effects of fine-scale heterogeneities by a macrodispersion term. It turned out that the new multi-scale algorithm represents a flexible and extendable tool for incorporating processes of different complexity occurring at different locations in one model domain, while reducing the amount of required data. Using a simplified numerical example, it could be shown that the multi-scale algorithm functions very well. However, more research has to be done in order to further improve its computational efficiency.

A Multiscale Model to Predict Slurry Erosion in Cavitated Duct Flows

In this work, a multiscale computational model of cavitation-erosion phenomena is proposed and performed in a Eulerian-Lagrangian two-way coupling approach. Cavitation-erosion phenomena are widely seen in multiphase flows with different sizes of time and length scale. Based on the multiscale concept, the information obtained at the level of small length scales can be used to provide closure information at the level of larger length scales. In our implementation, first a two-phase mixture flow model and a temperature-dependent homogeneous equilibrium saturation model are used to simulate phase transitions and steam–water interfaces. Subsequently, solid particle trajectories caused by the translation and rotation and particle–wall collisions are evaluated by a Lagrangian approach based on the continuum flow information. Then, a Eulerian-Lagrangian two-way coupling is used to evaluate the interactions between the gas–liquid mixture and dispersive solid particles, such as the drag, virtual mass, and lift forces. An erosion model is also implemented in this Eulerian-Lagrangian framework.

Weak lensing mass reconstruction using wavelets

This paper presents a new method for the reconstruction of weak lensing mass maps. It uses the multiscale entropy concept, which is based on wavelets, and the False Discovery Rate (FDR) which allows us to derive robust detection levels in wavelet space. We show that this new restoration approach outperforms several standard techniques currently used for weak shear mass reconstruction. This method can also be used to separate E and B modes in the shear field, and thus test for the presence of residual systematic effects. We concentrate on large blind cosmic shear surveys, and illustrate our results using simulated shear maps derived from N -Body Λ CDM simulations (Vale & White 2003) with added noise corresponding to both ground-based and space-based observations.

Enhanced-discretization Selective Stabilization Procedure (EDSSP)

The enhanced-discretization selective stabilization procedure (EDSSP) provides a multiscale framework for applying numerical stabilization selectively at different scales. The EDSSP is based on the enhanced-discretization, multiscale function space concept underlying the enhanced- discretization successive update method (EDSUM). The EDSUM is a multi-level iteration method designed for computation of the flow behavior at small scales. It has a built-in mechanism for transferring flow information between the large and small scales in a fashion consistent with the discretizations resulting from the underlying stabilized formulations. This is accomplished without assuming that the small-scale trial or test functions vanish at the borders between the neighboring large-scale elements of the enhanced-discretization zones. This facilitates unrestricted movement of small-scale flow patterns from one large-scale element to another without any constraints at the border between the two elements. The enhanced-discretization concept underlying the EDSUM can also facilitate using different stabilizations for equations or unknowns corresponding to different scales. In this paper we propose a version of the EDSSP where the SUPG and PSPG stabilizations are used for unknowns corresponding to both the large and small scales but the discontinuity-capturing stabilizations are used for unknowns corresponding to only the small scales. We also propose a version where a linear discontinuity-capturing is used for the small-scale unknowns and a nonlinear discontinuity-capturing is used for the large-scale unknowns. We evaluate the performances of these versions of the EDSSP with test problems governed by the advection–diffusion equations.

Wavelet and Multiscale Methods

The Wavelet and Multiscale Methods workshop, organized by Albert Cohen (Paris), Wolfgang Dahmen (Aachen), Ronald A. DeVore (Columbia) and Angela Kunoth (Bonn) was held July 11–17, 2004. A central objective was to bring together leading researchers working in a variety of different areas where multiscale phenomena play an intrinsic role regarding the theoretical understanding of the problems as well as the numerical solution concepts. This meeting was well attended with over 45 participants with a broad geographic representation from all continents. With only very few exceptions, the most prominent representers of the respective fields participated in the workshop. The main link being multiscale concepts, the overall audience was certainly less homogeneous than in most other workshops. In order to provide a solid ground for discussions and synergies, thirteen of the twenty six talks were longer survey-style lectures by leading experts who had been contacted by the organizers prior to the meeting. The following topics were addressed in the survey-type lectures: Several adaptive wavelet schemes for fluid flow problems were presented with varying emphasis on analysis and numerical realization. This included combinations of statistical and multiresolution concepts for understanding turbulence. Such approaches were complemented by a “two-scale” point of view where the concept of “residual free bubbles” allows one to model the influence of unresolved scales to the resolved ones, initiating vivid discussions about a possible combination of these approaches. From the perspective of nonlinear approximation, best N -term approximation in corresponding anisotropic function spaces was discussed, which is another important component in adaptive solution concepts in this context. Another focal point was the quasi – sparse or data – sparse representation of global operators, for instance, via wavelet bases or through concepts like hierarchical matrices. On one hand, this was shown to lead to new shape – optimization techniques as well as to significant advancements of adaptive wavelet methods for boundary integral equations. On the other hand, hierarchical matrix concepts were seen to make extremely high dimensional problems of a certain separable structure numerically tractable. In fact, problems of high spatial dimension were treated in the context of quantum chemistry centering upon the solution of the Schrödinger equation for many particles as one of the grand challenges of the future. Here compression and sparse grid techniques were again complemented by theoretical investigations of the regularity of eigensolutions which provides the foundation of the potential success of such numerical methods. Anisotropy is also a key issue in modern image compression techniques. The “wedgelet” concept was presented as a way of extending approximation libraries in combination with image encoding and model selection techniques. Moreover, the meeting adequately reflected through several talks some very recent advances in the currently highly active area of Mathematical Learning Theory, where new synergies between approximation theory and statistics are just emerging. In particular, wavelet techniques have now led to new universal estimators in a model free regression context where the universality could be achieved through nonlinear approximation concepts. Regarding the inhomogeneity of the participants' research fields, in order to maintain a high level of attendance and interest throughout the meeting, the topics of the lectures were deliberately mixed. This created a very open atmosphere and essentially all talks were followed by extensive discussions revealing a number of unforeseen connections between seemingly different subjects. The reaction of the participants during the meeting clearly indicated that the combination of different areas was very well perceived as a source of new ideas and perspectives. New collaborations were initiated and already existing cooperations partly across disciplines were pursued on a visibly intense level.

The future of stochastic and upscaling methods in hydrogeology

Geological formations are complex features resulting from geological, mechanical, and physico-chemical processes occurring over a very wide range of length scales and time scales. Transport phenomena ranging from the molecular scale to several hundreds of kilometers may influence the overall behavior of fluid flow in these formations. Heterogeneities that cover a large range of spatial scales play an essential role to channel fluid-flows, especially when they are coupled with non-linearities inherent to transport processes in porous media. These issues have considerable practical importance in groundwater management, and in the oil industry, particularly in solving new problems posed by projects concerned with the trapping of CO2 in the subsurface. In order to manage this complexity, one must be able to prioritize the respective influences of various relevant geological and physico-chemical phenomena occurring at several ranges of length and time scales as well as understand and use the increasingly rich and complex geostatistical models to provide realistic simulations of subsurface conditions. Multiscale simulation of fluid transport in these formations should help engineers to focus on the crucial phenomena that control the flow. This provides a natural framework to integrate data, to solve inverse problems involving large amounts of data, resulting in a reduction of the uncertainties of the subsurface description that must be evaluated. This allows in turn the making of more relevant practical decisions. In this paper, some perspectives on the development of upscaling approaches are presented, highlighting some recent multiscale concepts, discarding the fractured media case. Upscaling can be used as a useful framework to simultaneously manage scale-dependant problems, stochastic approaches and inverse problems. Actual and potential applications of upscaling to the elaboration of subsurface models constrained to observed data, and the management of uncertainties and sensitivity studies in a global multiscale framework is emphasized. In particular, upscaling can help in finding the parameters that control the overall behavior of the flow. Finally, upscaling approaches of non-linear transport equations appear as a new frontier in this area of research.

A Multi-Scale Modeling Concept and Computational Tools for the Integrative Analysis of Stationary Metabolic Data

SummaryMetabolic Engineering aims at the systematic analysis and targeted manipulation of the metabolism in biotechnologically utilized microorganisms [1,2]. Recently, consistent stationary in vivo data sets of intracellular metabolite concentrations, fluxes and specific enzyme activities have become available for this purpose [3,4]. For the integrative analysis of the metabolic data at hand, a novel multi-scale modeling concept, computeralgebraic methods and efficient numerical algorithms are proposed. The available metabolic data are typically afflicted with comparatively large measurement errors. Therefore, reliable comprehensive error estimations are essential for the reasonable interpretation of consecutive outcomes, such as simulation results. The concepts, methods and algorithms are first presented as universal methods and subsequently applied to the anaplerotic regulation in lysine-producing Corynebacterium glutamicum. A multi-scale model is set up, fitted to the available experimental data and validated by the prediction of further experiments. This model is capable of forecasting the quantitative effect of changes in the specific activity of anaplerotic enzymes, namely phosphoenolpyruvate carboxylase, pyruvate carboxylase and phosphoenolpyruvate carboxykinase, on lysine productivity and yield.

Identification of Microstructural Components of Bitumen by Means of Atomic Force Microscopy (AFM)

AbstractAccounting for the large variation of asphalt mixes, resulting from variations of constituents and composition, and from the allowance of additives, a multiscale model for asphalt is currently developed at the Christian Doppler Laboratory for “Performance‐based optimization of flexible road pavements”. The multiscale concept allows to relate macroscopic material properties of asphalt to phenomena and material properties of finer scales of observation. Starting with the characterization of the finest scale, i.e., the bitumen‐scale, Atomic Force Microscopy (AFM) is employed. Depending on the mode of measurement (tapping versus pulsed‐force mode), the AFM provides insight into the surface topography or stiffness and adhesion properties of bitumen. The obtained results will serve as input for upscaling in the context of the multiscale model in order to obtain the homogenized material behavior of bitumen at the next‐higher scale, i.e., the mastic‐scale. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Conservation properties for the Galerkin and stabilised forms of the advection–diffusion and incompressible Navier–Stokes equations

A common criticism of continuous Galerkin finite element methods is their perceived lack of conservation. This may in fact be true for incompressible flows when advective, rather than conservative, weak forms are employed. However, advective forms are often preferred on grounds of accuracy despite violation of conservation. It is shown here that this deficiency can be easily remedied, and conservative procedures for advective forms can be developed from multiscale concepts. As a result, conservative stabilised finite element procedures are presented for the advection–diffusion and incompressible Navier–Stokes equations.