Geodesic
Tensor-Product Discretization for the Spatially Inhomogeneous and Transient Boltzmann Equation in Two Dimensions
Grohs, Philipp1 ; Hiptmair, Ralf2 ; Pintarelli, Simon2
1 University of Vienna, Faculty of Mathematics
2 ETH Zürich, Seminar for Applied Mathematics
The SMAI Journal of computational mathematics, Tome 3 (2017), pp. 219-248

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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.

Publié le :
DOI : 10.5802/smai-jcm.26
Classification : 76J20, 76H05, 76P05, 82C40, 82D05, 65Y05, 65M60

Grohs, Philipp 1 ; Hiptmair, Ralf 2 ; Pintarelli, Simon 2

1 University of Vienna, Faculty of Mathematics
2 ETH Zürich, Seminar for Applied Mathematics 
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     author = {Grohs, Philipp and Hiptmair, Ralf and Pintarelli, Simon},
     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},
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     year = {2017},
     doi = {10.5802/smai-jcm.26},
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Grohs, Philipp; Hiptmair, Ralf; Pintarelli, Simon. Tensor-Product Discretization for the Spatially Inhomogeneous and Transient Boltzmann Equation in Two Dimensions. The SMAI Journal of computational mathematics, Tome 3 (2017), pp. 219-248. doi: 10.5802/smai-jcm.26

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