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Fourier transform approach to nonperiodic boundary value problems in porous conductive media
Author(s) -
To QuyDong,
Bonnet Guy,
NguyenThoi Trung
Publication year - 2021
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6749
Subject(s) - fourier transform , mathematical analysis , boundary value problem , mathematics , porous medium , thermal conduction , convergence (economics) , conductivity , fourier analysis , fourier series , porosity , physics , materials science , quantum mechanics , economics , composite material , thermodynamics , economic growth
In this article, we develop an extension of the Fourier transform solution method in order to solve conduction equation with nonperiodic boundary conditions (BC). The periodic Lippmann–Schwinger equation for porous materials is extended to the case of non‐periodicity with relevant source terms on the boundary. The method is formulated in Fourier space based on the temperature as unknown, using the exact periodic Green function and form factors to describe the boundaries. Different types of BC: flux, temperature, mixed and combined with periodicity can be treated by the method. Numerical simulations show that the method does not encounter convergence issues due to the infinite contrast and yields accurate results for both local fields and effective conductivity.