Higher order approximation methods for the Boltzmann equation

DOI10.1006/jcph.1997.5869zbMath0905.65134OpenAlexW2049493974MaRDI QIDQ1384501

Taku Ohwada

Publication date: 5 January 1999

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.1997.5869

zbMATH Keywords

finite difference methodBoltzmann equationsplitting methodhigher-order accuracytime difference method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05)

Related Items (14)

High order numerical methods for the space non-homogeneous Boltzmann equation. ⋮ Management of discontinuous reconstruction in kinetic schemes ⋮ On the numerical solution of a BGK-type model for chemical reactions ⋮ Lattice Boltzmann method and gas-kinetic BGK scheme in the low-Mach number viscous flow simulations. ⋮ A discrete velocity direction model for the Boltzmann equation and applications to micro gas flows ⋮ Solving the kinetic equation for all Knudsen numbers ⋮ Numerical solution of the Boltzmann equation using a fully conservative difference scheme based on the fast fourier transform ⋮ Asymptotic preserving Monte Carlo methods for the Boltzmann equation ⋮ A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann method ⋮ Fast spectral methods for the Fokker-Planck-Landau collision operator. ⋮ A numerical method for the accurate solution of the Fokker-Planck-Landau equation in the nonhomogeneous case ⋮ The kinetic scheme for the full-Burnett equations ⋮ The error of the splitting scheme for solving evolutionary equations ⋮ Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries

Cites Work

• The inclusion of collisional effects in the splitting scheme
• The mathematical theory of dilute gases
• Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules
• Direct simulation of gas flows at the molecular level
• Convergence of the total-approximation method for the Boltzmann equation
• Structure of normal shock waves: Direct numerical analysis of the Boltzmann equation for hard-sphere molecules
• A direct method for solving the Boltzmann equation
• On the Construction and Comparison of Difference Schemes

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