Numerical solutions of the Boltzmann equation: comparison of different algorithms |
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| Institution: | 1. Institute of Applied Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland;2. Università di Catania, Viale Andrea Doria 6, 95125 Catania, Italy;3. Institute of Fundamental Technological Research, Polish Academy of Science, Swietokrzyska 21, 00-049 Warszawa, Poland;1. Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria, 6-95125 Catania, Italy;2. Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan;1. Department of Mathematics, University of Mostaganem, Box 227, Mostaganem 27000, Algeria;2. Department of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong 510275, People’s Republic of China;3. Dipartimento di Mathematica e Informatica, Università di Catania, Viale Andrea Doria, 6, 95125 Catania, Italy;1. Dipartimento di Matematica e Informatica, Viale A. Doria, 6 - 95100 - Catania, Italy;2. Department of Mathematics, University of Nebraska–Lincoln, Lincoln, NE 68588-0130, USA;3. Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON P7B 5E1, Canada;1. Department of Mechanical, Aerospace & Biomedical Engineering, University of Tennessee Space Institute, 411 B.H. Goethert Parkway, MS 21, Tullahoma, TN 37388, USA;2. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA;1. Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 11, 91058, Erlangen, Germany.;2. Energie Campus Nürnberg, Fürther Straße 250, 90429, Nürnberg, Germany.;1. UJF-Grenoble 1/CNRS-INSU, Institut de Plantologie et d’Astrophysique de Grenoble (IPAG) UMR 5274, Grenoble F-38041, France;2. SSAI/NASA LaRC, Science Directorate, Chemistry and Dynamics Branch, 21 Langley Blvd., Mail Stop 401B, Hampton, VA 23681-2199, USA |
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| Abstract: | In the paper we compare different algorithms for numerical solutions of the Boltzmann equation. For this comparison we have taken the standard problem of the shock wave structure in a mono-atomic rarefied gas. Different parameters characterizing the shock structure have been calculated by a Monte Carlo simulation (DSMC), a second order time-relaxed Monte Carlo method (TRMC2), a fully deterministic discrete velocity method (DV), a discrete velocity method with Monte Carlo calculations of collision integral (DVMC) and a molecular dynamics method (MD). Results of these calculations have been compared with the shock wave structure obtained in experiments in a shock tube. The results of the comparison are not conclusive. We have observed general agreement between numerical and experimental results but there is no single numerical method which fits best to the experimental measurements. |
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