Numerical treatment of boundary conditions

1994 ◽  
pp. 196-216
Author(s):  
C. B. Vreugdenhil
Keyword(s):  
Boundary Conditions ◽  
Numerical Treatment

Proper Boundary Conditions for Infinitely Layered Orthotropic Media

2000 ◽  
Vol 67 (3) ◽  
pp. 629-632
Author(s):  
E. L. Bonnaud ◽  
J. M. Neumeister
Keyword(s):  
Boundary Conditions ◽  
Layered Medium ◽  
Integral Transforms ◽  
Numerical Treatment ◽  
Problem Size ◽  
Transfer Matrix Approach ◽  
Stress Functions ◽  
Orthotropic Media ◽  
First Time ◽  
Conditions At Infinity

A stress analysis of a plane infinitely layered medium subjected to surface loadings is performed using Airy stress functions, integral transforms, and a revised transfer matrix approach. Proper boundary conditions at infinity are for the first time established, which reduces the problem size by one half. Methods and approximations are also presented to enable numerical treatment and to overcome difficulties inherent to such formulations. [S0021-8936(00)01103-X]

Refinement in the Mathematical and Numerical Treatment of the Internal Oxidation of Alloys

2005 ◽  
Vol 237-240 ◽  
pp. 1157-1162 ◽  
Author(s):  
Wiktor Miszuris ◽  
Andreas Öchsner
Keyword(s):  
Boundary Conditions ◽  
Internal Oxidation ◽  
Diffusion Coefficients ◽  
Finite Dimension ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Numerical Treatment ◽  
Constant Diffusion ◽  
Finite Difference Solution ◽  
Oxide Particles

When oxygen dissolves from atmosphere and diffuses into an alloy during oxidation, the less noble alloy components may react to form oxide particles within the metal. This process is termed internal oxidation. Classical approaches to describe this phenomenon were derived under many strong simplifications such as constant diffusion coefficients, certain boundary conditions and semi-infinite sample. The presented general approach is based on the finite difference solution of the general diffusion equations coupled through the stoichiometry of reaction between oxygen and the considered element. The main enhancement is the consideration of concentration dependent diffusion coefficients, concentration dependent source terms and arbitrary time-dependent boundary conditions formulated as a concentration, a flux or mixed conditions. Furthermore, finite dimension of the specimen is incorporated. This general treatment also allows for the incorporation of the energy balance.

Numerical Treatment for the Coupled-BBM System

2016 ◽  
Vol 7 (2) ◽  
pp. 67 ◽  
Author(s):  
Khalid K. Ali ◽  
K. R. Raslan ◽  
Talaat S. EL-Danaf
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Solitary Waves ◽  
Nonlinear Term ◽  
Uniform Mesh ◽  
Test Accuracy ◽  
Numerical Treatment ◽  
Unconditionally Stable ◽  
Von Neumann ◽  
B Spline

// In the present paper, a numerical method is proposed for the numerical solution of a coupled-BBM system with appropriate initial and boundary conditions by using collocation method with quintic B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms \(L_2\), \(L_\infity\) are computed. Furthermore, interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves after the interaction. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.

Numerical treatment of boundary conditions at points connecting more than two electrically distinct regions

1987 ◽  
Vol 3 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Keith D. Paulsen ◽  
Daniel R. Lynch ◽  
John W. Strohbehn
Keyword(s):  
Boundary Conditions ◽  
Numerical Treatment
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