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CATEGORIES:Applied and Computational Analysis
SUMMARY:Deterministic Solution of the Boltzmann Equation:
Fast Spectral Methods for the Boltzmann Collision
Operator - Jingwei Hu\, Department of Mathematics\
, Purdue University
DTSTART;TZID=Europe/London:20190325T140000
DTEND;TZID=Europe/London:20190325T150000
UID:TALK121690AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/121690
DESCRIPTION:The Boltzmann equation\, an integro-differential e
quation for the molecular distribution function in
the physical and velocity phase space\, governs t
he fluid flow behavior at a wide range of physical
conditions. Despite its wide applicability\, dete
rministic numerical solution of the Boltzmann equa
tion presents a huge computational challenge due t
o the high-dimensional\, nonlinear\, and nonlocal
collision operator. We introduce a fast Fourier sp
ectral method for the Boltzmann collision operator
which leverages its convolutional and low-rank st
ructure. We show that the framework is quite gener
al and can be applied to arbitrary collision kerne
ls\, inelastic collisions\, and multiple species.
We then couple the fast spectral method in the vel
ocity space with the discontinuous Galerkin discre
tization in the physical space to obtain a highly
accurate deterministic solver for the full Boltzma
nn equation. Standard benchmark tests including ra
refied Fourier heat transfer\, Couette flow\, and
thermally driven cavity flow have been studied and
the results are compared against direct simulatio
n Monte Carlo (DSMC) solutions.
LOCATION:MR 14
CONTACT:Carola-Bibiane Schoenlieb
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