scholarly journals Convergence Rate of Monotone Numerical Schemes for Hamilton–Jacobi Equations with Weak Boundary Conditions

2008 ◽  
Vol 46 (5) ◽  
pp. 2371-2392 ◽  
Author(s):  
Knut Waagan
Keyword(s):  
Convergence Rate ◽  
Boundary Conditions ◽  
Numerical Schemes ◽  
Weak Boundary ◽  
Weak Boundary Conditions ◽  
Jacobi Equations

How to save a bad element with weak boundary conditions

2006 ◽  
Vol 35 (5) ◽  
pp. 477-484 ◽  
Author(s):  
Emmanuel Hanert ◽  
Vincent Legat
Keyword(s):  
Boundary Conditions ◽  
Weak Boundary ◽  
Weak Boundary Conditions

Elasticity Solutions to Nonbuckling Serpentine Ribbons

2016 ◽  
Vol 84 (2) ◽  
Author(s):  
Shixuan Yang ◽  
Shutao Qiao ◽  
Nanshu Lu
Keyword(s):  
Boundary Conditions ◽  
Electronic Materials ◽  
Beam Theory ◽  
Stretchable Electronics ◽  
Curved Beam ◽  
Weak Boundary ◽  
The Matrix ◽  
Elasticity Solutions ◽  
Weak Boundary Conditions ◽  
Total Curve

Stretchable electronics have found wide applications in bio-mimetic and bio-integrated electronics attributing to their softness, stretchability, and conformability. Although conventional electronic materials are intrinsically stiff and brittle, silicon and metal membranes can be patterned into in-plane serpentine ribbons for enhanced stretchability and compliance. While freestanding thin serpentine ribbons may easily buckle out-of-plane, thick serpentine ribbons may remain unbuckled upon stretching. Curved beam (CB) theory has been applied to analytically solve the strain field and the stiffness of freestanding, nonbuckling serpentine ribbons. While being able to fully capture the strain and stiffness of narrow serpentines, the theory cannot provide accurate solutions to serpentine ribbons whose widths are comparable to the arc radius. Here we report elasticity solutions to accurately capture nonbuckling, wide serpentine ribbons. We have demonstrated that weak boundary conditions are sufficient for solving Airy stress functions except when the serpentine’s total curve length approaches the ribbon width. Slightly modified weak boundary conditions are proposed to resolve this difficulty. Final elasticity solutions are fully validated by finite element models (FEM) and are compared with results obtained by the curved beam theory. When the serpentine ribbons are embedded in polymer matrices, their stretchability may be compromised due to the fact that the matrix can constrain the in-plane rotation of the serpentine. Comparison between the analytical solutions for freestanding serpentines and the FEM solutions for matrix-embedded serpentines reveals that matrix constraint remains trivial until the matrix modulus approaches that of the serpentine ribbon.

Modes of deformation and weak boundary conditions in wedge indentation

2012 ◽  
Vol 2 (2) ◽  
pp. 47-50 ◽  
Author(s):  
Narayan Sundaram ◽  
Yang Guo ◽  
Srinivasan Chandrasekar
Keyword(s):  
Boundary Conditions ◽  
Weak Boundary ◽  
Wedge Indentation ◽  
Weak Boundary Conditions ◽  
Image Position

Abstract

Changing the symmetry of a homogeneous instability with a change in temperature in a stationary shear flow of a nematic with weak boundary conditions in an electromagnetic field

2012 ◽  
Vol 9 (2) ◽  
pp. 101-106
Author(s):  
I.Sh Nasibullayev
Keyword(s):  
Electromagnetic Field ◽  
Liquid Crystal ◽  
Shear Flow ◽  
Boundary Conditions ◽  
Nematic Liquid Crystal ◽  
Numerical Study ◽  
Weak Boundary ◽  
Weak Boundary Conditions

In this work, a numerical study is made of the induced switching symmetry of a homogeneous instability by temperature in a stationary shear flow of a nematic liquid crystal under electromagnetic field with weak boundary conditions.

scholarly journals A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

2014 ◽  
Vol 16 (2) ◽  
pp. 345-358 ◽  
Author(s):  
Jan Nordström ◽  
Qaisar Abbas ◽  
Brittany A. Erickson ◽  
Hannes Frenander
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Finite Difference Methods ◽  
Difference Operators ◽  
Hyperbolic Problems ◽  
Order Of Accuracy ◽  
Weak Boundary ◽  
Difference Methods ◽  
Weak Boundary Conditions ◽  
High Order Finite Difference

AbstractA new weak boundary procedure for hyperbolic problems is presented. We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique. The new boundary procedure is applied near boundaries in an extended domain where data is known. We show how to raise the order of accuracy of the scheme, how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries. The new boundary procedure is cheap, easy to implement and suitable for all numerical methods, not only finite difference methods, that employ weak boundary conditions. Numerical results that corroborate the analysis are presented.

scholarly journals Multiphase CFD Modeling of External Oil Flow From a Journal Bearing

2018 ◽  
Author(s):  
Martin Berthold ◽  
Hervé Morvan ◽  
Richard Jefferson-Loveday ◽  
Benjamin C. Rothwell ◽  
Colin Young
Keyword(s):  
Boundary Conditions ◽  
Journal Bearing ◽  
Flow Behavior ◽  
Phase Interface ◽  
Numerical Schemes ◽  
Ansys Fluent ◽  
Oil Film ◽  
Reconstruction Scheme ◽  
Geometric Reconstruction ◽  
Oil Flow

High loads and bearing life requirements make journal bearings a potential choice for use in high power, epicyclic gearboxes in jet engines. Particularly in a planetary configuration the kinematic conditions are complex. With the planet gears rotating about their own axis and orbiting around the sun gear, centrifugal forces generated by both motions interact with each other and affect the external flow behavior of the oil exiting the journal bearing. Computational Fluid Dynamics (CFD) simulations using the Volume of Fluid (VoF) method are carried out in ANSYS Fluent [1] to numerically model the two-phase flow behavior of the oil exiting the bearing and merging into the air surrounding the bearing. This paper presents an investigation of two numerical schemes that are available in ANSYS Fluent to track or capture the air-oil phase interface: the geometric reconstruction scheme and the compressive scheme. Both numerical schemes are used to model the oil outflow behavior in the most simplistic approximation of a journal bearing: a representation, rotating about its own axis, with a circumferentially constant, i.e. concentric, lubricating gap. Based on these simplifications, a three dimensional (3D) CFD sector model with rotationally periodic boundaries is considered. A comparison of the geometric reconstruction scheme and the compressive scheme is presented with regards to the accuracy of the phase interface reconstruction and the time required to reach steady state flow field conditions. The CFD predictions are validated against existing literature data with respect to the flow regime, the direction of the predicted oil flow path and the oil film thickness. Based on the findings and considerations of industrial requirements, a recommendation is made for the most suitable scheme to be used. With a robust and partially validated CFD model in place, the model fidelity can be enhanced to include journal bearing eccentricity. Due to the convergent-divergent gap and the resultant pressure field within the lubricating oil film, the outflow behavior can be expected to be very different compared to that of a concentric journal bearing. Naturally, the inlet boundary conditions for the oil emerging from the journal bearing into the external environment must be consistent with the outlet conditions from the bearing. The second part of this paper therefore focuses on providing a method to generate appropriate inlet boundary conditions for external oil flow from an eccentric journal bearing.

Supplement to Numerical Schemes for Conservation Laws via Hamilton-Jacobi Equations

1995 ◽  
Vol 64 (210) ◽  
pp. S13
Author(s):  
L. Corrias ◽  
M. Falcone ◽  
R. Natalini
Keyword(s):  
Conservation Laws ◽  
Numerical Schemes ◽  
Jacobi Equations
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