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Accelerating the Convergence of the Moment Method for the Boltzmann Equation Using Filters

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Abstract

The moment method is a successful way to approximate the solution of the Boltzmann equation in reasonable runtime with relatively few unknowns while allowing for non-equilibrium effects of the gas. However, the convergence of the moment method with respect to an increasing number of moments is typically slow. This paper aims to improve the convergence of the moment method by introducing filtered hyperbolic moment equations that result in virtually no additional computational overhead while significantly reducing the error. The filter approach is based on a careful study of averaging solutions of two adjacent moment systems and the reformulation of the averaging using an artificial collision method that naturally gives rise to the filter. We study the properties of the filter and show numerical test cases of one-dimensional problems that demonstrate the superior quality of the new filtered moment method.

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Acknowledgements

The authors thank the referees for their constructive and helpful comments. The research of J. Koellermeier was funded by a joint postdoctoral scholarship from Freie Universität Berlin and Peking University.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, USA

    Yuwei Fan

  2. Institut für Mathematik, Freie Universität Berlin, Berlin, Germany

    Julian Koellermeier

  3. School of Mathematical Sciences, Peking University, Beijing, China

    Julian Koellermeier

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  1. Yuwei Fan
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  2. Julian Koellermeier
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Correspondence to Julian Koellermeier.

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Fan, Y., Koellermeier, J. Accelerating the Convergence of the Moment Method for the Boltzmann Equation Using Filters. J Sci Comput 84, 1 (2020). https://doi.org/10.1007/s10915-020-01251-8

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