An entropy stable discontinuous Galerkin finite-element moment method for the Boltzmann equation

DOI10.1016/j.camwa.2016.05.021zbMath1359.65192arXiv1602.01312OpenAlexW2256503782MaRDI QIDQ521830

M. R. A. Abdelmalik, E. Harald Van Brummelen

Publication date: 12 April 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.01312

zbMATH Keywords

Boltzmann equationentropy dissipationdiscontinuous Galerkin finite-element methodsmoment systems

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Statistical mechanics of gases (82D05) Boltzmann equations (35Q20)

Related Items

Simultaneous-approximation-term based boundary discretization for moment equations of rarefied gas dynamics ⋮ Moment method as a numerical solver: challenge from shock structure problems ⋮ Moment closure approximations of the Boltzmann equation based on \(\varphi \)-divergences ⋮ Entropy bounds for the space-time discontinuous Galerkin finite element moment method applied to the BGK-Boltzmann equation ⋮ Grad's distribution function for 13 moments-based moment gas kinetic solver for steady and unsteady rarefied flows: discrete and explicit forms ⋮ Finite elements in flow problems 2015 ⋮ Entropy stable Hermite approximation of the linearised Boltzmann equation for inflow and outflow boundaries ⋮ Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation ⋮ A discontinuous Galerkin fast spectral method for the full Boltzmann equation with general collision kernels

Uses Software

• HE-E1GODF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Moment closure approximations of the Boltzmann equation based on \(\varphi \)-divergences
• Mathematical aspects of discontinuous Galerkin methods.
• Compressible fluid flow and systems of conservation laws in several space variables
• Macroscopic transport equations for rarefied gas flows. Approximation methods in kinetic theory.
• From the Boltzmann equation to an incompressible Navier-Stokes-Fourier system
• Hydrodynamic limits of the Boltzmann equation
• A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation
• Hydrodynamic limit of the stationary Boltzmann equation in a slab
• The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
• Moment closure hierarchies for kinetic theories.
• On discontinuous Galerkin approximations of Boltzmann moment systems with Levermore closure
• Probability theory. A comprehensive course.
• A class of measures of informativity of observation channels
• Towards realizable hyperbolic moment closures for viscous heat-conducting gas flows based on a maximum-entropy distribution
• Maximisation of the entropy in non-equilibrium
• On the continuum equations for dispersed particles in nonuniform flows
• On the constitutive relations for dispersed particles in nonuniform flows. I: Dispersion in a simple shear flow
• Direct Simulation and the Boltzmann Equation
• On a kinetic equation for the transport of particles in turbulent flows
• On the kinetic theory of rarefied gases
• On Information and Sufficiency
• A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
• From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II

This page was built for publication: An entropy stable discontinuous Galerkin finite-element moment method for the Boltzmann equation