Numerical Solver for the Boltzmann Equation with Self-Adaptive Collision Operators

DOI10.1137/21M1398495zbMath1491.76049arXiv2102.08559OpenAlexW3131264590MaRDI QIDQ5065499

Zhenning Cai, Yan Li Wang

Publication date: 22 March 2022

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.08559

zbMATH Keywords

Boltzmann equationbinary collisionself-adaptationBGK approximationBurnett spectral methodheuristic error indicator

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Spectral methods applied to problems in fluid mechanics (76M22)

Uses Software

• HLLE

Cites Work

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• Locally refined discrete velocity grids for stationary rarefied flow simulations
• Deterministic solution of the spatially homogeneous Boltzmann equation using discontinuous Galerkin discretizations in the velocity space
• Approximation of the linearized Boltzmann collision operator for hard-sphere and inverse-power-law models
• Fluid simulations with localized Boltzmann upscaling by direct simulation Monte-Carlo
• Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement
• An efficient numerical method for solving the Boltzmann equation in multidimensions
• Numerical simulation of microflows using moment methods with linearized collision operator
• Galerkin-Petrov approach for the Boltzmann equation
• Regularity theory for the spatially homogeneous Boltzmann equation with cut-off
• Modeling and computational methods for kinetic equations
• A hybrid discontinuous Galerkin scheme for multi-scale kinetic equations
• On steady-state preserving spectral methods for homogeneous Boltzmann equations
• Burnett spectral method for the spatially homogeneous Boltzmann equation
• Approximation of the Boltzmann collision operator based on Hermite spectral method
• Slow rarefied flows. Theory and application to micro-electro-mechanical systems.
• 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
• A unified gas-kinetic scheme for continuum and rarefied flows. IV: Full Boltzmann and model equations
• Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier-Stokes asymptotics
• A smooth transition model between kinetic and hydrodynamic equations
• Polynomial expansions in kinetic theory of gases
• A Fourier spectral method for homogeneous boltzmann equations
• Solving the Boltzmann Equation in N log₂N
• Predicting continuum breakdown in hypersonic viscous flows
• On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
• Values of the nodes and weights of ninth to seventeenth order gauss-markov quadrature formulae invariant under the octahedron group with inversion
• Finite Volume Methods for Hyperbolic Problems
• A Polynomial Spectral Method for the Spatially Homogeneous Boltzmann Equation
• Regularized 13-moment equations for inverse power law models
• Burnett Spectral Method for High-Speed Rarefied Gas Flows
• Numerical Simulation of Microflows Using Hermite Spectral Methods
• A Hierarchy of Hybrid Numerical Methods for Multiscale Kinetic Equations
• A Fast Spectral Method for the Boltzmann Collision Operator with General Collision Kernels
• Moment realizability and the validity of the Navier–Stokes equations for rarefied gas dynamics
• On the kinetic theory of rarefied gases

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