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Effects of Anisotropy in Tridimensional Diffusion: Flow Patterns and Transport Efficiency

Modeling diffusive processes via a constant effective diffusivity value taken to represent realistic uncertainty or heterogeneity is entrenched in scientific and engineering applications. This brings forth the question, to what extent does the flow pattern changes when symmetry is broken by anisotropy. This study supplies the answer by deriving a class of tridimensional solutions to the steady nonlinear diffusion equation in a spherical domain divided into an arbitrary number of meridian sectors with distinct diffusivities and generation rates. The new family of solutions permits flexible modeling, where traditionally only isotropic radial transport was considered. The flow patterns support an extensive variety of topological terrain via tesseral and sectoral harmonics. The anisotropy gives rise to an unconventional type of a fixed point combining both node and saddle attributes. The contours are nonsmooth on the contiguity planes between sectors and might or might not be localized in the polar angle
and/or azimuthal angle , implying a particle might remain confined to a relatively small neighborhood or meander over the sphere. The impact on motion trajectories and thus transport efficiency implies that the energy required to sustain a steady flow is starkly underestimated when symmetry is assumed for simplicity despite the presence of anisotropy.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON APPLIED MATHEMATICS; Vol.83 No.2 March-April 2023

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 460-483

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

ANISOTROPY
EXACT SOLUTIONS
SPHERICAL COORDINATES
NONLINEAR DIFFUSION EQUATION
SECTORAL AND TESSERAL HARMONICS
TRANSPORT EFFICIENCY

Info Detail Spesifik

https://doi.org/10.1137/22M1476642

Pernyataan Tanggungjawab

Piyush Awasthi, Mahendhar Kumar, Yana Nec

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