Second-order diffusion limit for the phonon transport equation-asymptotics and numerics

Fuente: arXiv
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Main Authors: Nair, Anjali, Li, Qin, Sun, Weiran
Format: Preprint
Published: 2022
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author Nair, Anjali
Li, Qin
Sun, Weiran
author_facet Nair, Anjali
Li, Qin
Sun, Weiran
contents We investigate the numerical implementation of the limiting equation for the phonon transport equation in the small Knudsen number regime. The main contribution is that we derive the limiting equation that achieves the second order convergence, and provide a numerical recipe for computing the Robin coefficients. These coefficients are obtained by solving an auxiliary half-space equation. Numerically the half-space equation is solved by a spectral method that relies on the even-odd decomposition to eliminate corner-point singularity. Numerical evidences will be presented to justify the second order asymptotic convergence rate.
format Preprint
id arxiv_https___arxiv_org_abs_2201_07054
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Second-order diffusion limit for the phonon transport equation-asymptotics and numerics
Nair, Anjali
Li, Qin
Sun, Weiran
Numerical Analysis
We investigate the numerical implementation of the limiting equation for the phonon transport equation in the small Knudsen number regime. The main contribution is that we derive the limiting equation that achieves the second order convergence, and provide a numerical recipe for computing the Robin coefficients. These coefficients are obtained by solving an auxiliary half-space equation. Numerically the half-space equation is solved by a spectral method that relies on the even-odd decomposition to eliminate corner-point singularity. Numerical evidences will be presented to justify the second order asymptotic convergence rate.
title Second-order diffusion limit for the phonon transport equation-asymptotics and numerics
topic Numerical Analysis
url https://arxiv.org/abs/2201.07054