A high order space-momentum discontinuous Galerkin method for the Boltzmann equation

DOI10.1016/j.camwa.2015.06.011zbMath1443.65207OpenAlexW1131214893MaRDI QIDQ2006455

Joachim Schöberl, Gerhard Kitzler

Publication date: 11 October 2020

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2015.06.011

zbMATH Keywords

Boltzmann equationdiscontinuous Galerkin methodsspectral methodshigh order methods

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (11)

High-order hybridisable discontinuous Galerkin method for the gas kinetic equation ⋮ Multidisciplinary benchmarks of a conservative spectral solver for the nonlinear Boltzmann equation ⋮ A Polynomial Spectral Method for the Spatially Homogeneous Boltzmann Equation ⋮ Galerkin-Petrov approach for the Boltzmann equation ⋮ Very high order discontinuous Galerkin method in elliptic problems ⋮ Tensor-Product Discretization for the Spatially Inhomogeneous and Transient Boltzmann Equation in Two Dimensions ⋮ Implicit discontinuous Galerkin method for the Boltzmann equation ⋮ Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations ⋮ Application of discontinuous Galerkin method to mechanical 2D problem with arbitrary polygonal and very high-order finite elements ⋮ A high-order hybridizable discontinuous Galerkin method with fast convergence to steady-state solutions of the gas kinetic equation ⋮ Fully conservative spectral Galerkin-Petrov method for the inhomogeneous Boltzmann equation

Uses Software

• NGSolve

Cites Work

• A discontinuous Galerkin method for the Vlasov-Poisson system
• Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states
• Exact solutions of the nonlinear Boltzmann equation
• The mathematical theory of dilute gases
• Fast deterministic method of solving the Boltzmann equation for hard spheres
• A Fourier spectral method for homogeneous boltzmann equations
• Polynomial expansions for the isotropic Boltzmann equation and invariance of the collision integral with respect to the choice of basis functions
• On a simulation scheme for the Boltzmann equation
• Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator
• DISCONTINUOUS GALERKIN METHODS FOR THE MULTI-DIMENSIONAL VLASOV–POISSON PROBLEM
• Stochastic Numerics for the Boltzmann Equation
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