Tensor-Product Discretization for the Spatially Inhomogeneous and Transient Boltzmann Equation in Two Dimensions
The SMAI Journal of computational mathematics, Volume 3 (2017), pp. 219-248.

We consider the spatially inhomogeneous and nonlinear Boltzmann equation for the variable hard spheres model. The distribution function is discretized by a tensor-product ansatz by combining Maxwellian modulated Laguerre polynomials in velocity with continuous, linear finite elements in the spatial domain. The advection problem in phase space is discretized through a Galerkin least squares technique and yields an implicit formulation in time. The discrete collision operator can be evaluated with an asymptotic effort of 𝒪(K 5 ), where K is the number of velocity degrees of freedom in a single direction. Numerical results in 2D are presented for rarefied gases with different Mach and Knudsen numbers.

Published online:
DOI: 10.5802/smai-jcm.26
Classification: 76J20, 76H05, 76P05, 82C40, 82D05, 65Y05, 65M60
Philipp Grohs 1; Ralf Hiptmair 2; Simon Pintarelli 2

1 University of Vienna, Faculty of Mathematics
2 ETH Zürich, Seminar for Applied Mathematics
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Philipp Grohs and Ralf Hiptmair and Simon Pintarelli},
     title = {Tensor-Product {Discretization} for the {Spatially} {Inhomogeneous} and {Transient} {Boltzmann} {Equation} in {Two} {Dimensions}},
     journal = {The SMAI Journal of computational mathematics},
     pages = {219--248},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {3},
     year = {2017},
     doi = {10.5802/smai-jcm.26},
     zbl = {1416.82038},
     mrnumber = {3716757},
     language = {en},
     url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.26/}
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Philipp Grohs; Ralf Hiptmair; Simon Pintarelli. Tensor-Product Discretization for the Spatially Inhomogeneous and Transient Boltzmann Equation in Two Dimensions. The SMAI Journal of computational mathematics, Volume 3 (2017), pp. 219-248. doi : 10.5802/smai-jcm.26. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.26/

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