scholarly journals Convex Polygonal Hull for a Pair of Irregular Objects

2021 ◽  
pp. 13-24
Author(s):  
V.M. Dubynskyi ◽  
O.V. Pankratov ◽  
T.E. Romanova ◽  
B.S. Lysenko ◽  
R.V. Kayafyuk ◽  
...  
Keyword(s):  
Complex Geometry ◽  
Minimum Size ◽  
Function Technique ◽  
Two Dimensional ◽  
Packing Problems ◽  
Starting Point ◽  
Polygonal Region ◽  
Minimal Convex ◽  
Continuous Rotations ◽  
Feasible Solutions

Introduction. Optimization placement problems are NP-hard. In most cases related to cutting and packing problems, heuristic approaches are used. The development of analytical methods for mathematical modeling of the problems is of paramount important for expanding the class of placement problems that can be solved optimally using state of the art NLP-solvers. The problem of placing two irregular two-dimensional objects in a convex polygonal region of the minimum size, which is a convex polygonal hull of the minimum area or perimeter, is considered. Continuous rotations and translations of non-overlapping objects are allowed. To solve the problem of optimal compaction of a pair of objects, two algorithms are proposed. The first is a sequentially search for local extrema on all feasible subdomains using a solution tree. The second algorithm searches for a locally optimal extremum on a single subdomain using a "good" feasible starting point. Purpose of the paper. Show how to construct a minimal convex polygonal hull for two continuously moving irregular objects bounded by circular arcs and line segments. Results. A mathematical model is constructed in the form of a nonlinear programming problem using the phi-function technique. Two algorithms are proposed for solving the problem of placing a pair of objects in order to minimize the area and perimeter of the enclosing polygonal area. The results of computational experiments are presented. Conclusions. The construction of a minimal convex polygonal hull for a pair of two-dimensional objects having an arbitrary spatial shape and allowing continuous rotations and translations makes it possible to speed up the process of finding feasible solutions for the problem of placing a large number of objects with complex geometry. Keywords: convex polygonal hull, irregular objects, phi-function technique, nonlinear optimization.

Comparison of DSMC and CFD Models of Heat Transfer in a Rarefied Two-Dimensional Geometry

2018 ◽  
Author(s):  
Dilesh Maharjan ◽  
Mustafa Hadj-Nacer ◽  
Miles Greiner ◽  
Stefan K. Stefanov
Keyword(s):  
Heat Transfer ◽  
Rarefied Gas ◽  
Complex Geometry ◽  
Direct Simulation Monte Carlo ◽  
Accurate Method ◽  
Vacuum Drying ◽  
Helium Pressure ◽  
Two Dimensional ◽  
Dsmc Method ◽  
Cfd Simulations

During vacuum drying of used nuclear fuel (UNF) canisters, helium pressure is reduced to as low as 67 Pa to promote evaporation and removal of remaining water after draining process. At such low pressure, and considering the dimensions of the system, helium is mildly rarefied, which induces a thermal-resistance temperature-jump at gas–solid interfaces that contributes to the increase of cladding temperature. It is important to maintain the temperature of the cladding below roughly 400 °C to avoid radial hydride formation, which may cause cladding embrittlement during transportation and long-term storage. Direct Simulation Monte Carlo (DSMC) method is an accurate method to predict heat transfer and temperature under rarefied condition. However, it is not convenient for complex geometry like a UNF canister. Computational Fluid Dynamics (CFD) simulations are more convenient to apply but their accuracy for rarefied condition are not well established. This work seeks to validate the use of CFD simulations to model heat transfer through rarefied gas in simple two-dimensional geometry by comparing the results to the more accurate DSMC method. The geometry consists of a circular fuel rod centered inside a square cross-section enclosure filled with rarefied helium. The validated CFD model will be used later to accurately estimate the temperature of an UNF canister subjected to vacuum drying condition.

scholarly journals CFD Analysis of Urban Canopy Flows Employing the V2F Model: Impact of Different Aspect Ratios and Relative Heights

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Fabio Nardecchia ◽  
Annalisa Di Bernardino ◽  
Francesca Pagliaro ◽  
Paolo Monti ◽  
Giovanni Leuzzi ◽  
...  
Keyword(s):  
Flow Field ◽  
Water Channel ◽  
Flow Regimes ◽  
Two Dimensional ◽  
Mean Flow ◽  
Ansys Fluent ◽  
Practical Applications ◽  
Aspect Ratios ◽  
Starting Point ◽  
Step Down

Computational fluid dynamics (CFD) is currently used in the environmental field to simulate flow and dispersion of pollutants around buildings. However, the closure assumptions of the turbulence usually employed in CFD codes are not always physically based and adequate for all the flow regimes relating to practical applications. The starting point of this work is the performance assessment of the V2F (i.e., v2¯ − f) model implemented in Ansys Fluent for simulating the flow field in an idealized array of two-dimensional canyons. The V2F model has been used in the past to predict low-speed and wall-bounded flows, but it has never been used to simulate airflows in urban street canyons. The numerical results are validated against experimental data collected in the water channel and compared with other turbulence models incorporated in Ansys Fluent (i.e., variations of both k-ε and k-ω models and the Reynolds stress model). The results show that the V2F model provides the best prediction of the flow field for two flow regimes commonly found in urban canopies. The V2F model is also employed to quantify the air-exchange rate (ACH) for a series of two-dimensional building arrangements, such as step-up and step-down configurations, having different aspect ratios and relative heights of the buildings. The results show a clear dependence of the ACH on the latter two parameters and highlight the role played by the turbulence in the exchange of air mass, particularly important for the step-down configurations, when the ventilation associated with the mean flow is generally poor.

Heuristics for Two-Dimensional Bin-Packing Problems

2018 ◽  
pp. 27-1-27-18
Author(s):  
Tak Ming Chan ◽  
Filipe Alvelos ◽  
Elsa Silva ◽  
J.M. Valério de Carvalho
Keyword(s):  
Bin Packing ◽  
Two Dimensional ◽  
Packing Problems

scholarly journals Jamming and Geometric Representations of Graphs

10.37236/1082 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Werner Krauth ◽  
Martin Loebl
Keyword(s):  
Two Dimensional ◽  
Systematic Treatment ◽  
Packing Problems ◽  
Geometric Representations ◽  
Geometric Representations Of Graphs ◽  
Maximal Packing

We expose a relationship between jamming and a generalization of Tutte's barycentric embedding. This provides a basis for the systematic treatment of jamming and maximal packing problems on two-dimensional surfaces.

scholarly journals Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170612 ◽  
Author(s):  
Malena I. Español ◽  
Dmitry Golovaty ◽  
J. Patrick Wilber
Keyword(s):  
Continuum Model ◽  
Domain Walls ◽  
Three Dimensional ◽  
Variational Model ◽  
Dimensional System ◽  
Two Dimensional ◽  
Starting Point ◽  
Continuum Modelling ◽  
Three Dimensional System ◽  
The Continuum

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Two-Dimensional Bin Packing Problems

2013 ◽  
pp. 107-129 ◽  
Author(s):  
Andrea Lodi ◽  
Silvano Martello ◽  
Michele Monaci ◽  
Daniele Vigo
Keyword(s):  
Bin Packing ◽  
Two Dimensional ◽  
Packing Problems

scholarly journals Testing the effect of water in crevasses on a physically based calving model

2012 ◽  
Vol 53 (60) ◽  
pp. 90-96 ◽  
Author(s):  
S. Cook ◽  
T. Zwinger ◽  
I.C. Rutt ◽  
S. O'Neel ◽  
T. Murray
Keyword(s):  
Finite Element ◽  
Water Depth ◽  
Surface Mass Balance ◽  
Two Dimensional ◽  
Finite Element Code ◽  
Surface Mass ◽  
Starting Point ◽  
Physically Based ◽  
Calving Rate

AbstractA new implementation of a calving model, using the finite-element code Elmer, is presented and used to investigate the effects of surface water within crevasses on calving rate. For this work, we use a two-dimensional flowline model of Columbia Glacier, Alaska. Using the glacier’s 1993 geometry as a starting point, we apply a crevasse-depth calving criterion, which predicts calving at the location where surface crevasses cross the waterline. Crevasse depth is calculated using the Nye formulation. We find that calving rate in such a regime is highly dependent on the depth of water in surface crevasses, with a change of just a few metres in water depth causing the glacier to change from advancing at a rate of 3.5 kma–1 to retreating at a rate of 1.9 km a–1. These results highlight the potential for atmospheric warming and surface meltwater to trigger glacier retreat, but also the difficulty of modelling calving rates, as crevasse water depth is difficult to determine either by measurement in situ or surface mass-balance modelling.

scholarly journals Two Dimensional Model for Backwater Geomorphology: Darby Creek, PA

Water ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 2204 ◽  
Author(s):  
Hosseiny ◽  
Smith
Keyword(s):  
Urban Areas ◽  
Water Surface ◽  
Integrated Model ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Morphological Alterations ◽  
Digital Elevation ◽  
Starting Point ◽  
Spatio Temporal ◽  
Elevation Model

Predicting morphological alterations in backwater zones has substantial merit as it potentially influences the life of millions of people by the change in flood dynamics and land topography. While there is no two-dimensional river model available for predicting morphological alterations in backwater zones, there is an absolute need for such models. This study presents an integrated iterative two-dimensional fluvial morphological model to quantify spatio-temporal fluvial morphological alterations in normal flow to backwater conditions. The integrated model works through the following steps iteratively to derive geomorphic change: (1) iRIC model is used to generate a 2D normal water surface; (2) a 1D water surface is developed for the backwater; (3) the normal and backwater surfaces are integrated; (4) an analytical 2D model is established to estimate shear stresses and morphological alterations in the normal, transitional, and backwater zones. The integrated model generates a new digital elevation model based on the estimated erosion and deposition. The resultant topography then serves as the starting point for the next iteration of flow, ultimately modeling geomorphic changes through time. This model was tested on Darby Creek in Metro-Philadelphia, one of the most flood-prone urban areas in the US and the largest freshwater marsh in Pennsylvania.

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