scholarly journals Topological asymptotic formula for the 3D non-stationary Stokes problem and application

2020 ◽  
Vol Volume 32 - 2019 - 2020 ◽  
Author(s):  
Maatoug Hassine ◽  
Rakia Malek
Keyword(s):  
Asymptotic Expansion ◽  
Stokes System ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Detection Algorithm ◽  
International Audience ◽  
Flow Domain ◽  
Topological Asymptotic Expansion ◽  
Small Obstacle ◽  
Theoretical Results

International audience This paper is concerned with a topological asymptotic expansion for a parabolic operator. We consider the three dimensional non-stationary Stokes system as a model problem and we derive a sensitivity analysis with respect to the creation of a small Dirich-let geometric perturbation. The established asymptotic expansion valid for a large class of shape functions. The proposed analysis is based on a preliminary estimate describing the velocity field perturbation caused by the presence of a small obstacle in the fluid flow domain. The obtained theoretical results are used to built a fast and accurate detection algorithm. Some numerical examples issued from a lake oxygenation problem show the efficiency of the proposed approach. Ce papier porte sur l'analyse de sensibilité topologique pour un opérateur parabolique. On considère le problème de Stokes instationnaire comme un exemple de modèle et on donne une étude de sensibilité décrivant le comportement asymptotique de l'opérateur relativement à une petite perturbation géométrique du domaine. L'analyse présentée est basée sur une estimation du champ de vitesse calculée dans le domaine perturbé. Les résultats de cette étude ont servi de base pour développer un algorithme d'identification géométrique. Pour la validation de notre approche, on donne une étude numérique pour un problème d'optimisation d'emplacement des injecteurs dans un lac eutrophe. Des exemples numériques montrent l'efficacité de la méthode proposée

scholarly journals Shape optimization for the Stokes equations using topological sensitivity analysis

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Hassine Maatoug
Keyword(s):  
Sensitivity Analysis ◽  
Asymptotic Expansion ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Topological Sensitivity ◽  
Outflow Rate ◽  
International Audience ◽  
Small Obstacle

International audience In this paper, we consider a shape optimization problem related to the Stokes equations. The proposed approach is based on a topological sensitivity analysis. It consists in an asymptotic expansion of a cost function with respect to the insertion of a small obstacle in the domain. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the shape of the tubes that connect the inlet to the outlets of the cavity maximizing the outflow rate. Dans ce papier, on considère un problème d'optimisation de forme lié aux équations de Stokes. On propose une approche basée sur une analyse de sensibilité topologique. On donne un développement asymptotique d'une fonction coût par rapport à la perturbation du domaine par l'insertion d'un petit obstacle. Des résultats théoriques sont donnés en 2 D et 3 D. Dans la partie numérique, on utilise cette approche pour optimiser la forme des tubes liant l'entrée aux sorties d'une cavité

scholarly journals Topology Optimization of Time Dependent Viscous Incompressible Flows

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Maatoug Hassine
Keyword(s):  
Fluid Flow ◽  
Stokes System ◽  
Incompressible Flows ◽  
Navier Stokes ◽  
Dissipated Energy ◽  
Viscous Incompressible Flows ◽  
Topology And Shape Optimization ◽  
Design Function ◽  
Flow Domain ◽  
Small Obstacle

In this paper, we consider topology and shape optimization problem related to the nonstationary Navier-Stokes system. The minimization of dissipated energy in the fluid flow domain is discussed. The proposed approach is based on a sensitivity analysis of a design function with respect to the insertion of a small obstacle in the fluid flow domain. Some numerical results show the efficiency and accurate of the proposed approach.

ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE

2020 ◽  
Vol 7 (3) ◽  
pp. 52-56
Author(s):  
MMATMATISA JALILOV ◽  
◽  
RUSTAM RAKHIMOV ◽  
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Three Dimensional ◽  
Viscoelastic Plate ◽  
Constant Thickness ◽  
Regional Problem ◽  
Rigid Contact ◽  
Under Construction ◽  
Derivatives Of ◽  
Theoretical Results

This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.

scholarly journals Fast Overlap Detection between Hard-Core Colloidal Cuboids and Spheres. The OCSI Algorithm

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 72
Author(s):  
Luca Tonti ◽  
Alessandro Patti
Keyword(s):  
Colloidal Particles ◽  
Dynamic Properties ◽  
Wide Spectrum ◽  
Three Dimensional ◽  
Hard Core ◽  
Detection Algorithm ◽  
Three Dimensional Objects ◽  
Aggregation Behaviour ◽  
Sphere Radius ◽  
User Friendly

Collision between rigid three-dimensional objects is a very common modelling problem in a wide spectrum of scientific disciplines, including Computer Science and Physics. It spans from realistic animation of polyhedral shapes for computer vision to the description of thermodynamic and dynamic properties in simple and complex fluids. For instance, colloidal particles of especially exotic shapes are commonly modelled as hard-core objects, whose collision test is key to correctly determine their phase and aggregation behaviour. In this work, we propose the Oriented Cuboid Sphere Intersection (OCSI) algorithm to detect collisions between prolate or oblate cuboids and spheres. We investigate OCSI’s performance by bench-marking it against a number of algorithms commonly employed in computer graphics and colloidal science: Quick Rejection First (QRI), Quick Rejection Intertwined (QRF) and a vectorized version of the OBB-sphere collision detection algorithm that explicitly uses SIMD Streaming Extension (SSE) intrinsics, here referred to as SSE-intr. We observed that QRI and QRF significantly depend on the specific cuboid anisotropy and sphere radius, while SSE-intr and OCSI maintain their speed independently of the objects’ geometry. While OCSI and SSE-intr, both based on SIMD parallelization, show excellent and very similar performance, the former provides a more accessible coding and user-friendly implementation as it exploits OpenMP directives for automatic vectorization.

scholarly journals Generation and Annotation of Simulation-Real Ship Images for Convolutional Neural Networks Training and Testing

2021 ◽  
Vol 11 (13) ◽  
pp. 5931
Author(s):  
Ji’an You ◽  
Zhaozheng Hu ◽  
Chao Peng ◽  
Zhiqiang Wang
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Image Annotation ◽  
Three Dimensional ◽  
Image Data ◽  
Detection Algorithm ◽  
Simulation Software ◽  
High Quality ◽  
Annotation Method ◽  
Detection Of Objects

Large amounts of high-quality image data are the basis and premise of the high accuracy detection of objects in the field of convolutional neural networks (CNN). It is challenging to collect various high-quality ship image data based on the marine environment. A novel method based on CNN is proposed to generate a large number of high-quality ship images to address this. We obtained ship images with different perspectives and different sizes by adjusting the ships’ postures and sizes in three-dimensional (3D) simulation software, then 3D ship data were transformed into 2D ship image according to the principle of pinhole imaging. We selected specific experimental scenes as background images, and the target ships of the 2D ship images were superimposed onto the background images to generate “Simulation–Real” ship images (named SRS images hereafter). Additionally, an image annotation method based on SRS images was designed. Finally, the target detection algorithm based on CNN was used to train and test the generated SRS images. The proposed method is suitable for generating a large number of high-quality ship image samples and annotation data of corresponding ship images quickly to significantly improve the accuracy of ship detection. The annotation method proposed is superior to the annotation methods that label images with the image annotation software of Label-me and Label-img in terms of labeling the SRS images.

scholarly journals A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Niklas Ericsson
Keyword(s):  
Fourier Expansion ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Countable Family ◽  
Angular Variable ◽  
Two Dimensional ◽  
Sobolev Norms ◽  
Well Posed ◽  
Variational Formulations

Abstract We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems. By using decomposition of three-dimensional Sobolev norms, we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed. We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems.

Three Dimensional Detection of the via in the PCB CT Image Using Morphology Operation

2015 ◽  
Vol 752-753 ◽  
pp. 1406-1412
Author(s):  
Lei Zeng ◽  
Jian Chen ◽  
Han Ning Li ◽  
Bin Yan ◽  
Yi Fu Xu ◽  
...  
Keyword(s):  
Nondestructive Testing ◽  
Printed Circuit Board ◽  
Three Dimensional ◽  
Detection Algorithm ◽  
Circuit Board ◽  
Dimensional Structure ◽  
Three Dimension ◽  
Shape Information ◽  
Printed Circuit ◽  
Testing Technology

In modern industry, the nondestructive testing of printed circuit board (PCB) can prevent effectively the system failure and is becoming more and more important. As a vital part of the PCB, the via connects the devices, the components and the wires and plays a very important role for the connection of the circuits. With the development of testing technology, the nondestructive testing of the via extends from two dimension to three dimension in recent years. This paper proposes a three dimensional detection algorithm using morphology method to test the via. The proposed algorithm takes full advantage of the three dimensional structure and shape information of the via. We have used the proposed method to detect via from PCB images with different size and quality, and found the detection performances to be very encouraging.

Optimization of the Three-Dimensional Flow Path in the Scroll-Nozzle System of a Radial Inflow Turbine

1984 ◽  
Vol 106 (2) ◽  
pp. 511-515 ◽  
Author(s):  
E. A. Baskharone
Keyword(s):  
Flow Analysis ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Three Dimensional Flow ◽  
Multiply Connected ◽  
Dimensional Flow ◽  
Nozzle Configuration ◽  
Flow Domain ◽  
Radial Inflow Turbine ◽  
Compressibility Effects

A three-dimensional inviscid flow analysis in the combined scroll-nozzle system of a radial inflow turbine is presented. The coupling of the two turbine components leads to a geometrically complicated, multiply-connected flow domain. Nevertheless, this coupling accounts for the mutual effects of both elements on the three-dimensional flow pattern throughout the entire system. Compressibility effects are treated for an accurate prediction of the nozzle performance. Different geometrical configurations of both the scroll passage and the nozzle region are investigated for optimum performance. The results corresponding to a sample scroll-nozzle configuration are verified by experimental measurements.

Sign in / Sign up

Export Citation Format

Share Document