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Fast Numerical Method for 2D Initial-Boundary Value Problems for the Boltzmann Equation

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Parallel Processing and Applied Mathematics (PPAM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8385))

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Abstract

We present a new numerical scheme for the initial-boundary value problem for the Boltzmann equation in two-dimensional physical space. It is based on a splitting procedure in which the collision equation is solved using the adaptive algorithm for the computation of the full three-dimensional Boltzmann collision operator on non-uniform velocity grids introduced in the previous paper by the authors. The computation of the collision operator is performed in parallel for every physical grid cell. For the two-dimensional transport equation we use a second order finite volume method. The numerical example showing the effectiveness of our method is given.

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Authors and Affiliations

  1. Department of Mathematics, Chalmers University of Technology and Göteborg University, SE-412 96, Göteborg, Sweden

    Alexei Heintz

  2. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

    Piotr Kowalczyk

Authors
  1. Alexei Heintz
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  2. Piotr Kowalczyk
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Corresponding author

Correspondence to Piotr Kowalczyk .

Editor information

Editors and Affiliations

  1. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Department of Computer Science, Knoxville, Tennessee, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

  4. Technical University of Denmark Informatics and Mathematical Modelling, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Heintz, A., Kowalczyk, P. (2014). Fast Numerical Method for 2D Initial-Boundary Value Problems for the Boltzmann Equation. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55195-6_47

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  • DOI: https://doi.org/10.1007/978-3-642-55195-6_47

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55194-9

  • Online ISBN: 978-3-642-55195-6

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