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Tensor-product discretization for the spatially inhomogeneous and transient Boltzmann equation in 2D

by P. Grohs and R. Hiptmair and S. Pintarelli

(Report number 2015-38)

Abstract
In this paper we extend the previous work [E. Fonn, P. Grohs, and R. Hiptmair, Polar spectral scheme for the spatially homogeneous Boltzmann equation, Tech. Rep. 2014-13, Seminar for Applied Mathematics, ETH Zurich, 2014.] for the homogeneous nonlinear Boltzmann equation to the spatially inhomogeneous case. We employ a (Petrov)-Galerkin discretization in the velocity variable of the Boltzmann collision operator based on Laguerre polynomials times a Maxwellian. The advection problem in phase space is discretized by combining the spectral basis with continuous first order finite elements in space resulting in an implicit in time Galerkin least squares formulation. Numerical results in 2D are presented for different Mach and Knudsen numbers.

Keywords: Boltzmann equation, spectral methods, finite elements

@Techreport{GHP15_628,
  author = {P. Grohs and R. Hiptmair and S. Pintarelli},
  title = {Tensor-product discretization for the spatially inhomogeneous and transient Boltzmann equation in 2D},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2015-38},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-38.pdf },
  year = {2015}
}

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