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Fully conservative spectral Galerkin-Petrov method for the inhomogeneous Boltzmann equation. (English) Zbl 1421.82032

Summary: In this paper, we present an application of a Galerkin-Petrov method to the spatially one-dimensional Boltzmann equation. The three-dimensional velocity space is discretised by a spectral method. The space of the test functions is spanned by polynomials, which includes the collision invariants. This automatically insures the exact conservation of mass, momentum and energy. The resulting system of hyperbolic PDEs is solved with a finite volume method. We illustrate our method with two standard tests, namely the Fourier and the Sod shock tube problems. Our results are validated with the help of a stochastic particle method.

MSC:

82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
82C40 Kinetic theory of gases in time-dependent statistical mechanics
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
35L04 Initial-boundary value problems for first-order hyperbolic equations
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs

Software:

Boltzmann
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Full Text: DOI

References:

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