scholarly journals On the stability analysis of flows in channels of elliptic cross section using the finite element method on unstructured meshes

2020 ◽  
pp. 373-387
Author(s):  
Н.В. Клюшнев
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Cross Section ◽  
Unstructured Meshes ◽  
Flow Stability ◽  
Elliptic Cross Section ◽  
The Finite Element Method ◽  
Elliptic Cross ◽  
Element Method

Существующая технология численного анализа устойчивости течений вязкой несжимаемой жидкости в каналах постоянного сечения была ранее расширена на случай локальных пространственных аппроксимаций на неструктурированных сетках, приводящих к задачам с большими разреженными матрицами. Для пространственной аппроксимации при этом используется метод конечных элементов, а для решения частичных проблем собственных значений, возникающих при исследовании устойчивости течений, эффективный метод ньютоновского типа. В данной работе проводится подробное численное исследование предложенного подхода на примере двумерной конфигурации — течения Пуазейля в канале эллиптического сечения. Работоспособность подхода демонстрируется для широкого диапазона отношений длин полуосей сечения вплоть до отношения, при котором данное течение становится линейно неустойчивым. Показана сходимость ведущей части спектра по шагу сетки и совпадение результатов с результатами, полученными на основе аппроксимации спектральным методом коллокаций. The existing technique for the numerical analysis of incompressible fluid flow stability in channels of constant cross section was earlier extended to the case of local spatial approximations on unstructured meshes, which leads to large sparse matrices. The finite element method is employed for spatial approximation and a new efficient Newton-type method is used to solve partial eigenvalues problems arising in flow stability analysis. A detailed numerical study of the proposed approach is carried out in this paper by the example of Poiseuille flow in a channel of elliptic cross section. Performance ability of the approach is demonstrated for a wide range of the cross-sectional semiaxes ratio, including the case of linear instability of the flow under consideration. The convergence of the leading part of the spectrum with respect to the grid size is shown. Our results are in good agreement with those obtained via approximation by the spectral collocation method.

scholarly journals INTEGRATED SLOPE STABILITY ANALYSIS (SSA) WITH TRANSIENT GROUNDWATER FINITE ELEMENT METHOD FOR EMBANKMENT ANALYSIS

2021 ◽  
Vol 83 (5) ◽  
pp. 9-17
Author(s):  
Supandi Sujatono
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Slope Stability ◽  
Slope Stability Analysis ◽  
Clay Material ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Element Method ◽  
Storage Facilities

The content of level has a big enough role in the value of the physical characteristic and the mechanical of material. The behavior of water in these materials needs to be analyzed first in order to support the slope stability analysis. Modeling of water behavior in materials in the construction of Tailing Storage Facilities (TSF) will be integrated in the slope stability analysis. This study aims to provide an explanation about the analysis of the Fishing Storage Facilities (TSF) which integrates transient groundwater analysis using the finite element method in supporting the stability analysis of the embankment of Tailing Storage Facilities (TSF). The variables that are used in the analysis, they are the parameters of physical properties and mechanic material for embankment and permeability parameters in analyzing groundwater. The analysis method for geotechnical and geohydrology modeling uses the finite element method. The results of analysis showed that groundwater behavior in the embankment material can be known in detail so that it can be integrated with stability analysis.   It can be seen that there is a decrease in the value of the slope safety factor using the Integrated Slope Stability Analysis method compared to the conventional method. Adding an impermeable layer using a thickness of 5 m of clay material and a thickness of 20-30 m to support the retaining wall/foot is the criterion of optimal stability. The required lining material thickness (D) can be expressed by the following drawdown percentage equation function:  reduction percentage = (1-0.8661D (-0.031)) * 100%.  

Homogenization of multi-turn coil with elliptic cross-section using complex permeability

2019 ◽  
Vol 38 (3) ◽  
pp. 999-1008 ◽  
Author(s):  
Shogo Fujita ◽  
Hajime Igarashi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Cross Section ◽  
Fe Analysis ◽  
Complex Permeability ◽  
Elliptic Cross Section ◽  
Content Type ◽  
Elliptic Cross ◽  
Good Agreement

Purpose The tensor complex permeability of a multi-turn coil with elliptic cross-section is analytically expressed. In field analysis, a multi-turn coil can be modeled by the uniform material that has the present tensor complex permeability. It is shown that the frequency characteristic of the present tensor complex permeability is in good agreement with that evaluated by finite element method applied to a unit cell of the multi-turn coil region. Design/methodology/approach The authors introduce a new method to evaluate the complex permeability of a multi-turn rectangular coil. To obtain the complex permeability of a rectangular coil in a closed form, it is approximated as an elliptic coil. Because the rectangular coil has different complex permeabilities in the vertical and horizontal directions, the complex permeability have to be defined in a tensor form. It suffices to discretize the coil region into rather coarse finite elements without considering the skin depth in contrast to the conventional finite element method. Findings The proposed method is shown to give the impedance of multi-turn coils which is in good agreement with results obtained by the conventional finite element (FE) analysis. By extending the proposed approach, the authors can easily perform 3D FE analysis without difficulty in discretization of the coil region with fairly fine finite elements. Moreover, they found that the approximation of rectangular coils as the elliptic coils is valid for analysis of quasi-static fields using this homogenization method. Originality/value The novelty of this study is in the approximation of the rectangular coils with elliptic coils, and the complex permeability for them is formulated here in a closed form. The proposed formula includes that for the round coils. Using the present method, the authors analyze the rectangular coils without fine discretization.

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