Convection Problems on Anisotropic Meshes

2013 ◽  
Vol 13 (1) ◽  
pp. 55-78
Author(s):  
Carola Kruse ◽  
Matthias Maischak
Keyword(s):  
Steady State ◽  
Transport Problem ◽  
Annular Domain ◽  
Discontinuous Solutions ◽  
Continuous Solutions ◽  
Edge Singularity ◽  
Unit Square ◽  
Anisotropic Meshes ◽  
Theoretical Part ◽  
Convection Problem

Abstract. The Galerkin and SDFEM methods are compared for a steady state convection problem. The theoretical part of this work deals with the development of approximation results for continuous solutions on the unit square containing an edge singularity. In the numerical part we verify those approximation results by considering continuous as well as discontinuous solutions to the transport problem on an annular domain with a singularity at the inner circle.

System Dynamics of the Open-Draw With Web Adhesion: Particle Approach

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Sverker Edvardsson ◽  
Tetsu Uesaka
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Time Dependent ◽  
Temporal Fluctuation ◽  
Continuous Solutions ◽  
Continuous Growth ◽  
System Parameters ◽  
Paper Machines ◽  
Particle Approach ◽  
The Web

In the present work we propose a particle approach, which is designed to treat complex mechanics and dynamics of the open-draw sections that are still present in many of today’s paper machines. First, known steady-state continuous solutions are successfully reproduced. However, it is shown that since the boundary conditions depend on the solution itself, the solutions for web strain and web path in the open-draw section are generally time-dependent. With a certain set of system parameters, the nonsteady solutions are common. A temporal fluctuation of Young’s modulus, for example, destabilizes the system irreversibly, resulting in the continuous growth of web strain, i.e., break. Finally we exemplify with some strategic draw countermeasures how to prevent a dangerous evolution in the web strain.

Identification of a Steady-State Flow in Porous Media Using Artificial Neural Networks

2012 ◽  
Author(s):  
Marek J. Lefik ◽  
Daniela P. Boso ◽  
Bernhard A. Schrefler
Keyword(s):  
Neural Networks ◽  
Porous Media ◽  
Artificial Neural Networks ◽  
Steady State ◽  
Concentration Field ◽  
Flow In Porous Media ◽  
Homogeneous Field ◽  
Steady State Flow ◽  
Convection Problem ◽  
Artificial Neural

For a steady state convection problem, assuming given concentration field values in a few measurement points and hydraulic head values in the same piezometers, the source of the concentration, and its intensity are deduced using Artificial Neural Networks (ANNs). ANNs are trained with data extracted from Finite Difference (FD) solution of a classical convection problem for small Peclet number. The numerical analysis is exemplified for vanishing, homogeneous and non-homogeneous field of velocity. It is shown that the diffusivity vector can also be identified. The complexity of the problem is discussed for each studied case.

scholarly journals Ghizzetti's theorem for piecewise continuous solutions

1994 ◽  
Vol 17 (2) ◽  
pp. 283-286 ◽  
Author(s):  
Manuel Pinto
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Discontinuous Solutions ◽  
Continuous Solutions ◽  
Second Order Differential Equations ◽  
Piecewise Continuous ◽  
Straight Lines

We obtain that certain second order differential equations have discontinuous solutions which behaves asymptotically as straight lines.

scholarly journals Crystalline Oxide Solid Solutions in Oxygen Potential Gradients

1979 ◽  
Vol 34 (2) ◽  
pp. 192-199 ◽  
Author(s):  
H. Schmalzried ◽  
W. Laqua ◽  
P. L. Lin
Keyword(s):  
Solid Solution ◽  
Steady State ◽  
Numerical Solution ◽  
Solid Solutions ◽  
Potential Field ◽  
Oxygen Potential ◽  
Transport Problem ◽  
Oxide Solid Solution ◽  
Crystalline Oxide ◽  
Potential Gradients

Abstract The steady state demixing of an initially homogeneous oxide solid solution (A, B)O in an oxygen potential field is studied theoretically and experimentally.In case that DA > DB ≫ D0, the crystal is shifted with respect to the oxide lattice system toward the higher oxygen potential and is enriched in A at the side of the higher oxygen potential, while the transport of oxygen in the crystal is negligible. A numerical solution of the transport problem is presented, and the predicted effect is verified experimentally

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