A stochastic two-scale model for pressure-driven flow between rough surfaces

Seal surface topography typically consists of global-scale geometric features as well as local-scale roughness details and homogenization-based approaches are, therefore, readily applied. These provide for resolving the global scale (large domain) with a relatively coarse mesh, while resolving the local scale (small domain) in high detail. As the total flow decreases, however, the flow pattern becomes tortuous and this requires a larger local-scale domain to obtain a converged solution. Therefore, a classical homogenization-based approach might not be feasible for simulation of very small flows. In order to study small flows, a model allowing feasibly-sized local domains, for really small flow rates, is developed. Realization was made possible by coupling the two scales with a stochastic element. Results from numerical experiments, show that the present model is in better agreement with the direct deterministic one than the conventional homogenization type of model, both quantitatively in terms of flow rate and qualitatively in reflecting the flow pattern.

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Hydrodynamic Analysis of Macroalgae Local Model Using Computational Fluid Dynamics

Volume 6B: Ocean Engineering ◽

10.1115/omae2020-19279 ◽

2020 ◽

Author(s):

Ming Chen ◽

Solomon C. Yim ◽

Daniel Cox ◽

Zhaoqing Yang ◽

Thomas Mumford

Keyword(s):

Fluid Dynamics ◽

Experimental Data ◽

Computational Fluid Dynamics ◽

Current Model ◽

Global Scale ◽

Local Scale ◽

Constant Current ◽

Scale Model ◽

Effective Diameter ◽

Hydrodynamic Coefficients

Abstract In this article, a local scale, fully nonlinear coupled fluid-structural interaction (FSI) sugar kelp model has been developed using a computational fluid dynamics (CFD) method. In this model, to be consistent with available experimental data, the sugar kelp is approximated as elongated rectangles with smoothed isosceles triangles at the ends and a single kelp model with one end fixed in a channel with constant current model is developed. Several different current speeds are simulated, and the resulting drag forces and calculated drag coefficients are validated by comparison with experimental data from the literature. In a previous study, a global scale model was developed using a computational structural dynamics (CSD) method to simulate macroalgae farming system and guide the system configuration design. In the global scale model, the hydrodynamic forces are calculated using Morison’s equation and the kinematics and dynamics of the sugar kelp are simplified and the group of kelps attached to the long line is modeled as a slender structure with the same length and an effective diameter such that the volumes are consistent with the real physical system. This simplified model matches the weight and buoyancy but adjusting the hydrodynamic properties when the general hydrodynamic coefficients are employed. Therefore, optimal hydrodynamic coefficients used in global scale model were determined to obtain the hydrodynamic force more accurately. The validated local scale model is then be applied to determine the hydrodynamic coefficients of the simplified sugar kelp model for global dynamic analysis.

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A Stochastic Two-Scale Model for Rarefied Gas Flow in Highly Heterogeneous Porous Media

Transport in Porous Media ◽

10.1007/s11242-020-01476-z ◽

2020 ◽

Vol 135 (1) ◽

pp. 219-242

Author(s):

Francesc Pérez-Ràfols ◽

Fredrik Forsberg ◽

Gunnar Hellström ◽

Andreas Almqvist

Keyword(s):

Porous Medium ◽

Porous Media ◽

Gas Flow ◽

Present Model ◽

Rarefied Gas ◽

Slip Flow ◽

Local Scale ◽

Heterogeneous Porous Media ◽

Scale Model ◽

Rarefied Gas Flow

Abstract This paper presents the development of a model enabling the analysis of rarefied gas flow through highly heterogeneous porous media. To capture the characteristics associated with the global- and the local-scale topology of the permeable phase in a typical porous medium, the heterogeneous multi-scale method, which is a flexible framework for constructing two-scale models, was employed. The rapid spatial variations associated with the local-scale topology are accounted for stochastically, by treating the permeability of different local-scale domains as a random variable. The results obtained with the present model show that an increase in the spatial variability in the heterogeneous topology of the porous medium significantly reduces the relevance of rarefaction effects. This clearly shows the necessity of considering a realistic description of the pore topology and questions the applicability of the results obtained for topologies exhibiting regular pore patterns. Although the present model is developed to study low Knudsen number flows, i.e. the slip-flow regime, the same development procedure could be readily adapted for other regimes as well.

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A Multi-Scale Scheme for Modelling Fracture under Dynamic Loading Conditions

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.627.37 ◽

2014 ◽

Vol 627 ◽

pp. 37-40

Author(s):

A. Karamnejad ◽

L.J. Sluys

Keyword(s):

Dynamic Loading ◽

Static Problem ◽

Global Scale ◽

Local Scale ◽

Material Point ◽

Computational Homogenization ◽

Scale Model ◽

Multi Scale ◽

Damaged Zone ◽

Scale Scheme

Fracture in heterogeneous materials under dynamic loading is modelled using a multi-scale method. Computational homogenization is considered, in which the overall properties at the global-scale are obtained by solving a boundary value problem for a representative volume element (RVE) assigned to each material point of the global-scale model. In order to overcome the problems with upscaling of localized deformations, a non-standard failure zone averaging scheme is used. Discontinuous cohesive macro-cracking is modelled using the XFEM and a gradient-enhanced damage model is used to model diffuse damage at the local-scale. A continuous-discontinuous computational homogenization method is employed to obtain the traction-separation law for macro-cracks using averaged properties calculated over the damaged zone in the RVE. In the multi-scale model, a dynamic analysis is performed for the global-scale model and the local-scale model is solved as a quasi-static problem. Dispersion effects are then captured by accounting for the inertia forces at the local-scale model via a so-called dispersion tensor which depends on the heterogeneity of the RVE. Numerical examples are presented and the multi-scale model results are compared to direct numerical simulation results. Objectivity of the multi-scale scheme with respect to the RVE size is examined.

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On the loading and unloading of metal-to-metal seals: A two-scale stochastic approach

Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology ◽

10.1177/1350650118755620 ◽

2018 ◽

Vol 232 (12) ◽

pp. 1525-1537 ◽

Cited By ~ 3

Author(s):

Francesc Pérez-Ràfols ◽

Roland Larsson ◽

Egbert J van Riet ◽

Andreas Almqvist

Keyword(s):

Plastic Deformation ◽

Beneficial Effect ◽

Stochastic Approach ◽

Global Scale ◽

Scale Model ◽

Real Situation ◽

Metal Seal ◽

Flow Through ◽

Loading And Unloading ◽

Stochastic Element

During operation, the mating surfaces of a metal-to-metal seal typically undergo significant plastic deformation, which in turn can have beneficial effect on its performance. In previous studies, it has, for instance, been shown that plastic deformation can provide for better sealing during unloading. Those studies did, however, only consider flow through unrealistically small domains. Therefore, it is possible that this might be a size effect, which would not be apparent in a real situation with a much larger domain. In this paper, we develop a model which can handle real-sized seal domains at the same time as fine details of the surface topography. More precisely, we construct a two-scale model, in which the global scale represents the seal domain and where the influence of the fine details at the local scale are represented by a stochastic element. By means of this stochastic two-scale model, we show that the beneficial effect associated with the plastic deformation persists also when real-sized seal domains are considered.

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Double poroelasticity derived from the microstructure

Acta Mechanica ◽

10.1007/s00707-021-03030-4 ◽

2021 ◽

Author(s):

Laura Miller ◽

Raimondo Penta

Keyword(s):

Global Scale ◽

Homogenization Method ◽

Local Scale ◽

Scale Model ◽

The Novel ◽

Periodic Cell ◽

The Matrix ◽

Poroelastic Material ◽

The Given

AbstractWe derive the balance equations for a double poroelastic material which comprises a matrix with embedded subphases. We assume that the distance between the subphases (the local scale) is much smaller than the size of the domain (the global scale). We assume that at the local scale both the matrix and subphases can be described by Biot’s anisotropic, heterogeneous, compressible poroelasticity (i.e. the porescale is already smoothed out). We then decompose the spatial variations by means of the two-scale homogenization method to upscale the interaction between the poroelastic phases at the local scale. This way, we derive the novel global scale model which is formally of poroelastic-type. The global scale coefficients account for the complexity of the given microstructure and heterogeneities. These effective poroelastic moduli are to be computed by solving appropriate differential periodic cell problems. The model coefficients possess properties that, once proved, allow us to determine that the model is both formally and substantially of poroelastic-type. The properties we prove are a) the existence of a tensor which plays the role of the classical Biot’s tensor of coefficients via a suitable analytical identity and b) the global scale scalar coefficient $$\bar{\mathcal {M}}$$ M ¯ is positive which then qualifies as the global Biot’s modulus for the double poroelastic material.

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An Enhanced Stochastic Two-Scale Model for Metal-to-Metal Seals

Lubricants ◽

10.3390/lubricants6040087 ◽

2018 ◽

Vol 6 (4) ◽

pp. 87 ◽

Cited By ~ 2

Author(s):

Francesc Pérez-Ràfols ◽

Andreas Almqvist

Keyword(s):

Degrees Of Freedom ◽

Numerical Approach ◽

Global Scale ◽

Solution Procedure ◽

Local Scale ◽

Scale Model ◽

Length Scales ◽

Geometrical Features ◽

Mesh Density ◽

The Mathematical Model

Leakage in static metal-to-metal seals is predominantly determined by the topography of the contacting surfaces. The topography consists of features that span the entire range from its carefully engineered geometry down to micro-sized surface asperities. The mesh density necessary to fully resolve all the features, in this large span of length scales, generates too many degrees of freedom for a direct numerical approach to be applicable. Some kind of sophistication, either incorporated in the mathematical model or in the numerical solution procedure or even a combination of both is therefore required. For instance, in a two-scale model, the geometrical features can be addressed in the global-scale model, while the features belonging to length scales smaller than a given cut-off value are addressed in the local-scale model. However, the classical two-scale approaches do not explicitly address the stochastic nature of the surfaces, and this has turned out to be a requirement in order to obtain quantitative predictions of leakage in metal-to-metal seals. In this work, we present a continued development of an already existing two-scale model, which incorporates a stochastic element. The novelty lies in the way we characterise the permeability at the local scale and how this is used to build a more efficient and useful approach.

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8-Day and Daily Maximum and Minimum Air Temperature Estimation via Machine Learning Method on a Climate Zone to Global Scale

Remote Sensing ◽

10.3390/rs13122355 ◽

2021 ◽

Vol 13 (12) ◽

pp. 2355

Author(s):

Linglin Zeng ◽

Yuchao Hu ◽

Rui Wang ◽

Xiang Zhang ◽

Guozhang Peng ◽

...

Keyword(s):

Spatial Scale ◽

Air Temperature ◽

Spatial Scales ◽

Model Performance ◽

Global Scale ◽

Scale Model ◽

Validation Dataset ◽

Daily Maximum ◽

Climate Zone ◽

Temporal And Spatial

Air temperature (Ta) is a required input in a wide range of applications, e.g., agriculture. Land Surface Temperature (LST) products from Moderate Resolution Imaging Spectroradiometer (MODIS) are widely used to estimate Ta. Previous studies of these products in Ta estimation, however, were generally applied in small areas and with a small number of meteorological stations. This study designed both temporal and spatial experiments to estimate 8-day and daily maximum and minimum Ta (Tmax and Tmin) on three spatial scales: climate zone, continental and global scales from 2009 to 2018, using the Random Forest (RF) method based on MODIS LST products and other auxiliary data. Factors contributing to the relation between LST and Ta were determined based on physical models and equations. Temporal and spatial experiments were defined by the rules of dividing the training and validation datasets for the RF method, in which the stations selected in the training dataset were all included or not in the validation dataset. The RF model was first trained and validated on each spatial scale, respectively. On a global scale, model accuracy with a determination coefficient (R2) > 0.96 and root mean square error (RMSE) < 1.96 °C and R2 > 0.95 and RMSE < 2.55 °C was achieved for 8-day and daily Ta estimations, respectively, in both temporal and spatial experiments. Then the model was trained and cross-validated on each spatial scale. The results showed that the data size and station distribution of the study area were the main factors influencing the model performance at different spatial scales. Finally, the spatial patterns of the model performance and variable importance were analyzed. Both daytime and nighttime LST had a significant contribution in the 8-day Tmax estimation on all the three spatial scales; while their contribution in daily Tmax estimation varied over different continents or climate zones. This study was expected to improve our understanding of Ta estimation in terms of accuracy variations and influencing variables on different spatial and temporal scales. The future work mainly includes identifying underlying mechanisms of estimation errors and the uncertainty sources of Ta estimation from a local to a global scale.

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Carbon monoxide (CO) and ethane (C<sub>2</sub>H<sub>6</sub>) trends from ground-based solar FTIR measurements at six European stations, comparison and sensitivity analysis with the EMEP model

Atmospheric Chemistry and Physics ◽

10.5194/acp-11-9253-2011 ◽

2011 ◽

Vol 11 (17) ◽

pp. 9253-9269 ◽

Cited By ~ 38

Author(s):

J. Angelbratt ◽

J. Mellqvist ◽

D. Simpson ◽

J. E. Jonson ◽

T. Blumenstock ◽

...

Keyword(s):

Transport Model ◽

Global Scale ◽

Global Model ◽

Scale Model ◽

Chemical Transport Model ◽

Suitable Alternative ◽

European Model ◽

Time Period ◽

Volatile Organic ◽

Made In

Abstract. Trends in the CO andC2H6 partial columns ~0–15 km) have been estimated from four European ground-based solar FTIR (Fourier Transform InfraRed) stations for the 1996–2006 time period. The CO trends from the four stations Jungfraujoch, Zugspitze, Harestua and Kiruna have been estimated to −0.45 ± 0.16% yr−1, −1.00 ± 0.24% yr−1, −0.62 ± 0.19 % yr−1 and −0.61 ± 0.16% yr−1, respectively. The corresponding trends for C2H6 are −1.51 ± 0.23% yr−1, −2.11 ± 0.30% yr−1, −1.09 ± 0.25% yr−1 and −1.14 ± 0.18% yr−1. All trends are presented with their 2-σ confidence intervals. To find possible reasons for the CO trends, the global-scale EMEP MSC-W chemical transport model has been used in a series of sensitivity scenarios. It is shown that the trends are consistent with the combination of a 20% decrease in the anthropogenic CO emissions seen in Europe and North America during the 1996–2006 period and a 20% increase in the anthropogenic CO emissions in East Asia, during the same time period. The possible impacts of CH4 and biogenic volatile organic compounds (BVOCs) are also considered. The European and global-scale EMEP models have been evaluated against the measured CO and C2H6 partial columns from Jungfraujoch, Zugspitze, Bremen, Harestua, Kiruna and Ny-Ålesund. The European model reproduces, on average the measurements at the different sites fairly well and within 10–22% deviation for CO and 14–31% deviation for C2H6. Their seasonal amplitude is captured within 6–35% and 9–124% for CO and C2H6, respectively. However, 61–98% of the CO and C2H6 partial columns in the European model are shown to arise from the boundary conditions, making the global-scale model a more suitable alternative when modeling these two species. In the evaluation of the global model the average partial columns for 2006 are shown to be within 1–9% and 37–50% of the measurements for CO and C2H6, respectively. The global model sensitivity for assumptions made in this paper is also analyzed.

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Global‐ and Local‐Scale High‐Resolution Event Catalogs for Algorithm Testing

Seismological Research Letters ◽

10.1785/0220180345 ◽

2019 ◽

Cited By ~ 1

Author(s):

Lisa Linville ◽

Ronald Chip Brogan ◽

Christopher Young ◽

Katherine Anderson Aur

Keyword(s):

Global Scale ◽

Local Scale ◽

Algorithm Performance ◽

Directional Information ◽

Event Sequences ◽

University Of Utah ◽

International Monitoring ◽

Using Data ◽

The University ◽

Global And Local

ABSTRACT During the development of new seismic data processing methods, the verification of potential events and associated signals can present a nontrivial obstacle to the assessment of algorithm performance, especially as detection thresholds are lowered, resulting in the inclusion of significantly more anthropogenic signals. Here, we present two 14 day seismic event catalogs, a local‐scale catalog developed using data from the University of Utah Seismograph Stations network, and a global‐scale catalog developed using data from the International Monitoring System. Each catalog was built manually to comprehensively identify events from all sources that were locatable using phase arrival timing and directional information from seismic network stations, resulting in significant increases compared to existing catalogs. The new catalogs additionally contain challenging event sequences (prolific aftershocks and small events at the detection and location threshold) and novel event types and sources (e.g., infrasound only events and long‐wall mining events) that make them useful for algorithm testing and development, as well as valuable for the unique tectonic and anthropogenic event sequences they contain.

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Networks of Photos, Landmarks, and People

Leonardo ◽

10.1162/leon_a_00172 ◽

2011 ◽

Vol 44 (3) ◽

pp. 240-243 ◽

Cited By ~ 6

Author(s):

David Crandall ◽

Noah Snavely

Keyword(s):

Recent Work ◽

Human Behavior ◽

Visual Representations ◽

3D Models ◽

Global Scale ◽

Local Scale ◽

Photo Sharing ◽

The World ◽

Vantage Points ◽

Combining Information

Social photo-sharing sites like Flickr contain vast amounts of latent information about the world and human behavior. The authors describe their recent work in building automatic algorithms that analyze large collections of imagery in order to extract some of this information. At a global scale, geo-tagged photographs can be used to identify the most photographed places on Earth, as well as to infer the names and visual representations of these places. At a local scale, the authors build detailed 3D models of a scene by combining information from thousands of 2D photographs taken by different people and from different vantage points.

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