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SUMMARY:Towards an entropic method for the Boltzmann equation - Zhenning C
 ai (National University of Singapore)
DTSTART:20220523T133000Z
DTEND:20220523T143000Z
UID:TALK173417@talks.cam.ac.uk
DESCRIPTION:H-theorem is one of the important properties of the Boltzmann 
 equation\, which states the non-decreasing property of the Gibbs entropy. 
 In this work\, we are interested in finding a numerical scheme of the Bolt
 zmann equation that preserves this property. For the spatially homogeneous
  Boltzmann equation\, we consider a modification of the Fourier spectral m
 ethod from the perspective of discrete velocity method\, to achieve a seco
 nd-order velocity discretization with the structure of detailed balance. T
 he method allows one to readily apply the FFT-based fast algorithms\, and 
 it preserves positivity of the distribution function due to the applicatio
 n of a positive preserving limiter. As for the temporal discretization\, w
 e adopt a simple entropy fix by a convex combination of the current numeri
 cal solution and the equilibrium state. Such an entropy fix can be general
 ized to a wider class of ODE systems. It is proven that the entropy fix ha
 s only infinitesimal influence on the numerical order of the original sche
 me\, and in many circumstances\, it can be shown that the scheme does not 
 affect the numerical order. The work on the spatially inhomogeneous case i
 s ongoing. We will present some preliminary results on the analysis of the
  discontinuous Galerkin method.
LOCATION:Seminar Room 1\, Newton Institute
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