A framework for hyperbolic approximation of kinetic equations using quadrature-based projection methods

Julian Koellermeier*, Roman Pascal Schaerer, Manuel Torrilhon

*Bijbehorende auteur voor dit werk

OnderzoeksoutputAcademicpeer review

40 Citaten (Scopus)

Samenvatting

We derive hyperbolic PDE systems for the solution of the Boltzmann Equation. First, the velocity is transformed in a non-linear way to obtain a Lagrangian velocity phase space description that allows for physical adaptivity. The unknown distribution function is then approximated by a series of basis functions.
Standard continuous projection methods for this approach yield PDE systems for the basis coefficients that are in general not hyperbolic. To overcome this problem, we apply quadrature-based projection methods which modify the structure of the system in the desired way so that we end up with a hyperbolic system of equations.
With the help of a new abstract framework, we derive conditions such that the emerging system is hyperbolic and give a proof of hyperbolicity for Hermite ansatz functions in one dimension together with Gauss-Hermite quadrature.
Originele taal-2English
Pagina's (van-tot) 531-549
Aantal pagina's18
TijdschriftKinetic & Related Models
Volume7
Nummer van het tijdschrift3
DOI's
StatusPublished - 2014
Extern gepubliceerdJa

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