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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Towards an entropic method for the Boltzmann equat
ion - Zhenning Cai (National University of Singapo
re)
DTSTART;TZID=Europe/London:20220523T143000
DTEND;TZID=Europe/London:20220523T153000
UID:TALK173417AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/173417
DESCRIPTION:H-theorem is one of the important properties of th
e Boltzmann equation\, which states the non-decrea
sing property of the Gibbs entropy. In this work\,
we are interested in finding a numerical scheme o
f the Boltzmann equation that preserves this prope
rty. For the spatially homogeneous Boltzmann equat
ion\, we consider a modification of the Fourier sp
ectral method from the perspective of discrete vel
ocity method\, to achieve a second-order velocity
discretization with the structure of detailed bala
nce. The method allows one to readily apply the FF
T-based fast algorithms\, and it preserves positiv
ity of the distribution function due to the applic
ation of a positive preserving limiter. As for the
temporal discretization\, we adopt a simple entro
py fix by a convex combination of the current nume
rical solution and the equilibrium state. Such an
entropy fix can be generalized to a wider class of
ODE systems. It is proven that the entropy fix ha
s only infinitesimal influence on the numerical or
der of the original scheme\, and in many circumsta
nces\, it can be shown that the scheme does not af
fect the numerical order. The work on the spatiall
y inhomogeneous case is ongoing. We will present s
ome preliminary results on the analysis of the dis
continuous Galerkin method.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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