Fourier transform approach to nonperiodic boundary value problems in porous conductive media

Quy‐dong To (1, 2) , Guy Bonnet (1) , Trung Nguyen-Thoi (2)

1 MSME - Laboratoire Modélisation et Simulation Multi-Echelle
2 Ton Duc Thang University [Hô-Chi-Minh-City]

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.

Mots clés: Fourier transform; nonperiodic problems; numerical homogenization

Domaines: Mécanique des solides [physics.class-ph]; Physique mathématique [math-ph]

Quy‐dong To, Guy Bonnet, Trung Nguyen-Thoi. Fourier transform approach to nonperiodic boundary value problems in porous conductive media. International Journal for Numerical Methods in Engineering, 2021, 122 (18), pp.4864-4885. ⟨10.1002/nme.6749⟩. ⟨hal-03263301⟩