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Title: A fast conservative spectral solver for the nonlinear Boltzmann collision operator

We present a conservative spectral method for the fully nonlinear Boltzmann collision operator based on the weighted convolution structure in Fourier space developed by Gamba and Tharkabhushnanam. This method can simulate a broad class of collisions, including both elastic and inelastic collisions as well as angularly dependent cross sections in which grazing collisions play a major role. The extension presented in this paper consists of factorizing the convolution weight on quadrature points by exploiting the symmetric nature of the particle interaction law, which reduces the computational cost and memory requirements of the method to O(M{sup 2}N{sup 4}logN) from the O(N{sup 6}) complexity of the original spectral method, where N is the number of velocity grid points in each velocity dimension and M is the number of quadrature points in the factorization, which can be taken to be much smaller than N. We present preliminary numerical results.
Authors:
;  [1] ;  [2]
  1. Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Stop C1200 Austin, Texas 78712, USA and ICES, The University of Texas at Austin, 201 E. 24th St., Stop C0200, Austin, TX 78712 (United States)
  2. Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907, USA and ICES, The University of Texas at Austin, 201 E. 24th St., Stop C0200, Austin, TX 78712 (United States)
Publication Date:
OSTI Identifier:
22390540
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1628; Journal Issue: 1; Conference: 29. International Symposium on Rarefied Gas Dynamics, Xi'an (China), 13-18 Jul 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOLTZMANN EQUATION; COLLISION INTEGRALS; COLLISIONS; CROSS SECTIONS; ELASTIC SCATTERING; FACTORIZATION; INELASTIC SCATTERING; MATHEMATICAL OPERATORS; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; PARTICLE INTERACTIONS; QUADRATURES; SPACE; SYMMETRY; VELOCITY