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Models and numerical methods for time- and energy-dependent particle transport

Abstract

Particles passing through a medium can be described by the Boltzmann transport equation. Therein, all physical interactions of particles with matter are given by cross sections. We compare different analytical models of cross sections for photons, electrons and protons to state-of-the-art databases. The large dimensionality of the transport equation and its integro-differential form make it analytically difficult and computationally costly to solve. In this work, we focus on the following approximative models to the linear Boltzmann equation: (i) the time-dependent simplified P{sub N} (SP{sub N}) equations, (ii) the M{sub 1} model derived from entropy-based closures and (iii) a new perturbed M{sub 1} model derived from a perturbative entropy closure. In particular, an asymptotic analysis for SP{sub N} equations is presented and confirmed by numerical computations in 2D. Moreover, we design an explicit Runge-Kutta discontinuous Galerkin (RKDG) method to the M{sub 1} model of radiative transfer in slab geometry and construct a scheme ensuring the realizability of the moment variables. Among other things, M{sub 1} numerical results are compared with an analytical solution in a Riemann problem and the Marshak wave problem is considered. Additionally, we rigorously derive a new hierarchy of kinetic moment models in the context of grey photon  More>>
Authors:
Publication Date:
Apr 13, 2012
Product Type:
Thesis/Dissertation
Report Number:
ETDE-DE-2785
Resource Relation:
Other Information: TH: Diss. (Dr.rer.nat.)
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ANALYTICAL SOLUTION; BENCHMARKS; BOLTZMANN EQUATION; COMPARATIVE EVALUATIONS; ELECTRONS; ENTROPY; GALERKIN-PETROV METHOD; MATTER; NUMERICAL ANALYSIS; PERTURBATION THEORY; PHOTONS; PROTONS; RADIANT HEAT TRANSFER; RIEMANN FUNCTION; RUNGE-KUTTA METHOD; SCATTERING; TIME DEPENDENCE; TRANSPORT THEORY
OSTI ID:
22008277
Research Organizations:
RWTH Aachen Univ. (Germany). Fakultaet fuer Mathematik, Informatik und Naturwissenschaften
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
TRN: DE12GD485
Availability:
Commercial reproduction prohibited. Available from ETDE as OSTI ID: 22008277;
Submitting Site:
DE
Size:
187 page(s)
Announcement Date:
Jan 03, 2013

Citation Formats

Olbrant, Edgar. Models and numerical methods for time- and energy-dependent particle transport. Germany: N. p., 2012. Web.
Olbrant, Edgar. Models and numerical methods for time- and energy-dependent particle transport. Germany.
Olbrant, Edgar. 2012. "Models and numerical methods for time- and energy-dependent particle transport." Germany.
@misc{etde_22008277,
title = {Models and numerical methods for time- and energy-dependent particle transport}
author = {Olbrant, Edgar}
abstractNote = {Particles passing through a medium can be described by the Boltzmann transport equation. Therein, all physical interactions of particles with matter are given by cross sections. We compare different analytical models of cross sections for photons, electrons and protons to state-of-the-art databases. The large dimensionality of the transport equation and its integro-differential form make it analytically difficult and computationally costly to solve. In this work, we focus on the following approximative models to the linear Boltzmann equation: (i) the time-dependent simplified P{sub N} (SP{sub N}) equations, (ii) the M{sub 1} model derived from entropy-based closures and (iii) a new perturbed M{sub 1} model derived from a perturbative entropy closure. In particular, an asymptotic analysis for SP{sub N} equations is presented and confirmed by numerical computations in 2D. Moreover, we design an explicit Runge-Kutta discontinuous Galerkin (RKDG) method to the M{sub 1} model of radiative transfer in slab geometry and construct a scheme ensuring the realizability of the moment variables. Among other things, M{sub 1} numerical results are compared with an analytical solution in a Riemann problem and the Marshak wave problem is considered. Additionally, we rigorously derive a new hierarchy of kinetic moment models in the context of grey photon transport in one spatial dimension. For the perturbed M{sub 1} model, we present numerical results known as the two beam instability or the analytical benchmark due to Su and Olson and compare them to the standard M{sub 1} as well as transport solutions.}
place = {Germany}
year = {2012}
month = {Apr}
}