Polynomial preserving virtual elements with curved edges

2020 ◽  
Vol 30 (08) ◽  
pp. 1555-1590 ◽  
Author(s):  
L. Beirão da Veiga ◽  
F. Brezzi ◽  
L. D. Marini ◽  
A. Russo
Keyword(s):  
Theoretical Analysis ◽  
Patch Test ◽  
Small Scale ◽  
Intermediate Scale ◽  
Numerical Tests ◽  
Polynomial Preserving ◽  
Virtual Element

In this paper, we tackle the problem of constructing conforming Virtual Element spaces on polygons with curved edges. Unlike previous VEM approaches for curvilinear elements, the present construction ensures that the local VEM spaces contain all the polynomials of a given degree, thus providing the full satisfaction of the patch test. Moreover, unlike standard isoparametric FEM, this approach allows to deal with curved edges at an intermediate scale, between the small scale (treatable by homogenization) and the bigger one (where a finer mesh would make the curve flatter and flatter). The proposed method is supported by theoretical analysis and numerical tests.

scholarly journals Theoretical and experimental studies of a gas stamping device with a piston pressure multiplier

2019 ◽  
Vol 18 (1) ◽  
pp. 163-173
Author(s):  
A. Yu. Botashev ◽  
R. A. Bayramukov
Keyword(s):  
Theoretical Analysis ◽  
Experimental Studies ◽  
Fuel Mixture ◽  
Small Scale ◽  
Scale Production ◽  
Pressure Treatment ◽  
Energy Of Combustion ◽  
Stamping Process ◽  
Pressure Multiplier ◽  
The Matrix

In many industries, the share of small-scale production plants is significant. In these conditions, compared with traditional methods of pressure treatment, pulse pressure treatment methods, one of the varieties of which is gas stamping, are more efficient. However, the known devices of gas stamping provide mainly stamping of thin-walled parts. To expand the technological capabilities of gas stamping, the authors developed a gas stamping device with a piston pressure multiplier, in which heating and deformation of the stamping workpiece is carried out using the energy of combustion of fuel mixtures in the combustion chamber, in the working cylinder and in the cavity of the matrix. This article is devoted to the study of the workflow of this device. Theoretical analysis of the workflow was carried out, and, as a result, a pattern was determined for the variation of the pressure that performs the stamping process in the working cylinder. In particular, it was found that at the final stage of the stamping process, due to the energy of combustion of the fuel mixture, the pressure in the working cylinder increases 1.5...2 times, which allows a significant increase in the thickness of the parts to be stamped. An experimental gas stamping device with a piston pressure multiplier was developed, and experimental studies were carried out. The studies confirmed the main results of the theoretical analysis: the discrepancy between the theoretical and experimental values of the degree of pressure multiplication in the working cylinder does not exceed 11%.

scholarly journals The seismo-hydro-mechanical behaviour during deep geothermal reservoir stimulations: open questions tackled in a decameter-scale in-situ stimulation experiment

2017 ◽  
Author(s):  
Florian Amann ◽  
Valentin Gischig ◽  
Keith Evans ◽  
Joseph Doetsch ◽  
Reza Jalali ◽  
...  
Keyword(s):  
Rock Mass ◽  
Geothermal Energy ◽  
Numerical Models ◽  
Test Site ◽  
Crystalline Rock ◽  
Coupled Processes ◽  
Small Scale ◽  
Intermediate Scale ◽  
Grimsel Test Site

Abstract. In this contribution we present a review of scientific research results that address seismo-hydro-mechanical coupled processes relevant for the development of a sustainable heat exchanger in low permeability crystalline rock and introduce the design of the In-situ Stimulation and Circulation (ISC) experiment at the Grimsel Test Site dedicated to study such processes under controlled conditions. The review shows that research on reservoir stimulation for deep geothermal energy exploitation has been largely based on laboratory observations, large-scale projects and numerical models. Observations of full-scale reservoir stimulations have yielded important results. However, the limited access to the reservoir and limitations in the control on the experimental conditions during deep reservoir stimulations is insufficient to resolve the details of the hydro-mechanical processes that would enhance process understanding in a way that aids future stimulation design. Small scale laboratory experiments provide a fundamental insights into various processes relevant for enhanced geothermal energy, but suffer from 1) difficulties and uncertainties in upscaling the results to the field-scale and 2) relatively homogeneous material and stress conditions that lead to an over-simplistic fracture flow and/or hydraulic fracture propagation behaviour that is not representative for a heterogeneous reservoir. Thus, there is a need for intermediate-scale hydraulic stimulation experiments with high experimental control that bridge the various scales, and for which access to the target rock mass with a comprehensive monitoring system is possible. Only few intermediate-scale hydro-shearing and hydro-fracturing experiments have recently been performed in a densely instrumented rock mass. No such measurements have been performed on faults in crystalline basement rocks. The In-situ Stimulation and Circulation (ISC) experiment currently performed in a naturally fractured and faulted crystalline rock mass at the Grimsel Test Site (Switzerland) is designed to address open research questions, which could not be investigated in the required detail so far. Two hydraulic injection phases were executed to enhance the permeability of the rock mass: a hydro-shearing phase and then a hydraulic fracturing phase. During the injection phases the rock mass deformation across fractures and within intact rock, the pore pressure distribution and propagation and the micro-seismic response were monitored at a high spatial and temporal resolution.

Small-scale experimental and theoretical analysis on maximum temperature beneath ceiling in tunnel fire with vertical shafts

2017 ◽  
Vol 114 ◽  
pp. 537-544 ◽  
Author(s):  
Yan Fu Wang ◽  
Xiao Fei Sun ◽  
Biao Li ◽  
Tao Qin ◽  
Shuai Liu ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Maximum Temperature ◽  
Small Scale ◽  
Tunnel Fire

An inequality formulation of conformational energy differences

1976 ◽  
Vol 54 (4) ◽  
pp. 526-530 ◽  
Author(s):  
Johannes Pieter Colpa ◽  
H. Bernhard Schlegel ◽  
Saul Wolfe
Keyword(s):  
Theoretical Analysis ◽  
Transition State ◽  
Geometry Optimization ◽  
Energy Difference ◽  
Basis Set ◽  
Lower State ◽  
Energy Minimum ◽  
Numerical Tests ◽  
Pyramidal Inversion ◽  
True Energy

A theoretical analysis has been performed of the effects of geometry optimization upon computed barriers to rotation and pyramidal inversion. It is shown that, where ΔE is the true energy difference between the energy minimum and the transition state for a particular conformational process, (barrier using the optimized geometry of the lower state) > ΔE > (barrier using the optimized geometry of the higher state). Some numerical tests of this inequality are discussed. These reveal certain limitations upon the assumption that an optimized geometry is transferable from one basis set to another.

Strong interactions between two corotating quasi-geostrophic vortices

2007 ◽  
Vol 592 ◽  
pp. 117-133 ◽  
Author(s):  
ROSS R. BAMBREY ◽  
JEAN N. REINAUD ◽  
DAVID G. DRITSCHEL
Keyword(s):  
Strong Interaction ◽  
Volume Ratio ◽  
The Self ◽  
Strong Interactions ◽  
Small Scale ◽  
Filamentary Structure ◽  
Intermediate Scale ◽  
Margin Of Stability ◽  
Vortex Interactions ◽  
Aspect Ratios

In this paper we investigate the interaction between two corotating quasi-geostrophic vortices. The initially ellipsoidal vortices are separated horizontally by a distance corresponding to the margin of stability, as determined from an ellipsoidal analysis. The subsequent interaction depends on four parameters: the vortex volume ratio, the vertical centroid separation, and the height-to-width aspect ratios of each vortex. The most commonly observed strong interaction is partial merger, where only part of the weaker vortex is incorporated into the stronger one or cast into filamentary debris. Despite the proliferation of small-scale filamentary structure during many vortex interactions, on average the self-induced vortex energy exhibits an ‘inverse cascade’ to larger scales, broadly consistent with spectral theories of turbulence. Curiously, we observe that a range of intermediate-scale vortices are preferentially sheared out during the interactions, leaving two main populations of large and small vortices.

Three-dimensional wavelet analysis on turbulent structure of dune wake flow

2015 ◽  
Vol 13 (06) ◽  
pp. 1550045 ◽  
Author(s):  
Yan Zheng ◽  
Akira Rinoshika ◽  
Shun Fujimoto
Keyword(s):  
Coherent Structure ◽  
Large Scale ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Turbulent Structure ◽  
Wake Flow ◽  
Small Scale ◽  
Intermediate Scale ◽  
Numerical Result ◽  
Scale Structures

The three-dimensional (3D) turbulent structure was simulated by large eddy simulation (LES), and then the numerical result was validated by PIV experiment. In order to give a detailed description of dune wake flow, the instantaneous velocity, vorticity, and pressure were decomposed into the large-, intermediate- and relatively small-scale components by 3D wavelet multi-resolution technique. To get a further understanding of coherent structure, the decomposed wavelet components were employed to calculate Q-criterion. It was found that the rollers and horse-shoe structures in the separation bubble were mainly contributed from large-scale structures and it made the most significance to the vorticity concentration. The observations of intermediate-scale horse-shoe structures indicated that the coherent structure was the combined effect of large- and intermediate-scale structures. Besides, from the visualization of 3D streamlines and pressure iso-surfaces, the separation bubble and pressure distribution are found to be dominated by large-scale structure.

scholarly journals Analysis of the Relevant Parameters on Small Scale of Navigable Abnormal Ship Model

2017 ◽  
Vol 24 (s2) ◽  
pp. 133-139 ◽  
Author(s):  
Cai Chuang ◽  
Lei Penghua ◽  
Cai Xinyong
Keyword(s):  
Theoretical Analysis ◽  
Normal Mode ◽  
Similarity Theory ◽  
Similarity Criterion ◽  
Hydraulic Model ◽  
Small Scale ◽  
Variable Rate ◽  
Ship Maneuvering ◽  
Ship Model ◽  
Dimensional Effect

Abstract At present, ship model tests are based on the normal mode at home and abroad. With the development and application of abnormal hydraulic model, it is necessary to study abnormal ship model. The similarity criterion of abnormal ship model is deduced from the similarity theory of normal hydraulic model in this paper. Some factors that affect the maneuverability of the abnormal ship model are discussed by theoretical analysis of ship maneuvering. The influence of the K and T index of different variable rate on the abnormal ship model maneuvering and the dimensional effect of the abnormal ship model are obtained, which can be used as a reference for the study of the abnormal ship model.

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