Discussion of a “New” Elliptic Linear Boundary Condition with Applications to Hydrodynamics

1988 ◽  
Vol 48 (6) ◽  
pp. 1281-1286
Author(s):  
Michael Magen
Keyword(s):  
Boundary Condition ◽  
Linear Boundary ◽  
Linear Boundary Condition

scholarly journals Homogenization of a Conductive and Radiative Heat Transfer Problem, Simulation With CAST3M

2005 ◽  
Author(s):  
K. El Ganaoui ◽  
G. Allaire
Keyword(s):  
Boundary Condition ◽  
Radiative Heat ◽  
Transfer Problem ◽  
Computer Code ◽  
Homogenization Theory ◽  
Linear Boundary ◽  
Mathematical Study ◽  
Linear Boundary Condition ◽  
The Core ◽  
Homogenous Medium

We are interested in conductive and radiative transfer of energy in the core of gas cooled reactors. Two scales characterize the problem: macroscopic and microscopic. We want to consider the domain like an equivalent homogenous medium. So we use homogenization theory to compute the effective macroscopic properties which take into account the microscopic structure. We first present a full mathematical study of a simpler conduction problem with non linear boundary condition and its simulation with the CEA’s (French Atomic Energy Commissariat) computer code CAST3M. Then we present the homogenization of the real physical problem (including radiative boundary condition).

The theory of symmetrical gravity waves of finite amplitude. I

1951 ◽  
Vol 208 (1095) ◽  
pp. 475-486 ◽  
Keyword(s):  
Boundary Condition ◽  
Gravity Waves ◽  
Finite Amplitude ◽  
Breaking Wave ◽  
Two Dimensional ◽  
Linear Boundary ◽  
Dimensional Problem ◽  
Infinite Depth ◽  
Linear Boundary Condition ◽  
Small Parameters

The two-dimensional problem of symmetric finite amplitude gravity waves in an incompressible fluid of infinite depth is treated by a method which first involves satisfying a non-linear boundary condition exactly. The higher approximations are obtained by the method of small parameters. The breaking-wave conditions are discussed and expressions are given for the free-surface equation, the kinetic and the potential energies of the fluid.

Polynomial approximations to the solution of the heat equation

1973 ◽  
Vol 73 (1) ◽  
pp. 157-165 ◽  
Author(s):  
R. E. Scraton
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Partial Differential Equation ◽  
Exact Solution ◽  
Heat Equation ◽  
Least Squares ◽  
Linear Boundary ◽  
Chebyshev Series ◽  
Linear Boundary Condition ◽  
Image Position

AbstractAn approximation is found to the solution of the partial differential equationin the region −1 ≤ x ≤ 1, t > 0, where u satisfies a general linear boundary condition on x = ± 1. This approximation is a polynomial in x, and is an exact solution of a perturbed form of the differential equation. By choosing the perturbation appropriately, this approach is mathematically equivalent to some recent methods for solving the differential equation in the form of a Chebyshev series. Better approximations to the required solution (and particularly to the eigenvalues) are obtained by choosing the perturbation to satisfy a least squares criterion.

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